So the solution to the system of equations y = mx - 1 and y = (m - 1)x - 2 is the ordered pair (3, y). To find y, we simplify again and see that: y = 3 (Graham's Number) - 5. So the lines will intersect at (3, y) where y is an extremely big number. Jan 6, 2020 · Answer. Exercise 5.3.9 5.3. 9. Solve the system by elimination. {3x + 2y = 2 6x + 5y = 8 { 3 x + 2 y = 2 6 x + 5 y = 8. Answer. Now we’ll do an example where we need to multiply both equations by constants in order to make the coefficients of one variable opposites. Title: Infinitely many solutions for a class of fractional Schrodinger equations coupled with neutral scalar field. Authors: Liejun Shen, Marco Squassina, Xiaoyu Zeng. …Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints. Gravity Printech India Private Limited | 161 followers on LinkedIn. Barcode Label Application Solutions | Gravity Printech is a reliable hub offering durable and affordable printing …Jul 18, 2022 · The lines coincide; they intersect at infinitely many points. This is a dependent system. The figures below show all three cases. Every system of equations has either one solution, no solution, or infinitely many solutions. In the last section, we used the Gauss-Jordan method to solve systems that had exactly one solution. A system of 2 linear equations in 2 variables has infinitely many solutions when the two lines have the same slope and the same y-intercept (that is, the two equations are equivalent and represent the same line, so they intersect at every point on the line). A system of equations in 2, 3, or more variables can have infinite solutions.Infinitely many solutions. Let’s look now at a system of equations with infinitely many solutions. While it will not always be so obvious, you can tell that this system has infinitely many solutions because the second equation is just a multiple of the first. \(\begin{array}{l} x+y=-2\\ \\2x+2y=-4\end{array}\)Dec 20, 2023 ... B = 0, system is consistent, with infinitely many solutions. ⇒ If det (A) = 0 and (adj A). B ≠ 0, system is inconsistent (no solution).For what values of k will the following pair of linear equations have infinitely many solutions? kx + 3y - (k – 3) = 0 12x + ky - k = 0. Solution: In the above equation a 1 = k, a 2 = 12, b 1 = 3, b 2 = k, c 1 = -(k - 3) and c 2 = -k. If a solution has infinitely many solutions, then. ⇒ a 1 / a 2 = b 1 / b 2 = c 1 / c 2 . For the above pair ...Infinitely many solutions. Let’s look now at a system of equations with infinitely many solutions. While it will not always be so obvious, you can tell that this system has infinitely many solutions because the second equation is just a multiple of the first. \(\begin{array}{l} x+y=-2\\ \\2x+2y=-4\end{array}\)When we graph systems of equations, the intersection of the lines is the solution. If a system has infinitely many solutions, then the lines overlap at every point. In other words, they're the same exact line! This means that any point on the line is a solution to the system. Thus, the system of equations above has infinitely many solutions. For a pair of linear equations to have infinitely many solutions: `a_1/a_2 = b_1/b_2 = c_1/c_2` So, we need `k/12 = 3/k = (k - 3)/k` or `k/12 = 3/k` Which gives k 2 = 36, i.e., k = ± 6. Also, `3/k = (k - 3)/k` Gives 3k = k 2 – 3k, i.e., 6k = k 2, which means k = 0 or k = 6. Therefore, the value of k, that satisfies both the conditions, is k = 6. For this value, the …1 Answer. If a2 + 3a − 4 = 0 a 2 + 3 a − 4 = 0 and −3a + 3 = 0 − 3 a + 3 = 0 then you will have infinitely many solutions. If a2 + 3a − 4 = 0 a 2 + 3 a − 4 = 0 and −3a + 3 ≠ 0 − 3 a + 3 ≠ 0, then you will not have any solutions. The point is that a row (0 0 0 1) ( 0 0 0 1) will correspond to the equation 0x1 + 0x2 + 0x3 = 1 ...Consider a consistent linear system, then the system must have infinitely many solutions. True. False. Check. Reuse ...Infinitely many positive solutions for Kirchhoff equations with competing coefficients Published: 05 March 2019 Volume 70 , article number 53 , ( 2019 )Modified 9 years, 11 months ago. Viewed 2k times. 1. The question asks to find equation for which the system has infinitely many solutions. The system is: ⎧⎩⎨−cx + 3y + 2z = 8 x + z = 2 3x + 3y + az = b { − c x + 3 y + 2 z = 8 x + z = 2 3 x + 3 y + a z = b. How should I approach questions like this?Infinitely Many Solutions or No Solution? Equations Special Cases - YouTube © 2024 Google LLC How to know if an equation has Infinitely Many Solutions or No Solution? We look at these 2... To have infinitely many solutions, we want our equation and $5x - 2y = 3$ to intersect everywhere. In other words, they will be the same line. One way to denote this is to simply use the same equation, $5x - 2y = 3$, or just multiply both sides of the equation by a constant; let’s say we multiply each term by 2. Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 3x-5y = 20 ; 6x-10y =40. Q. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions.If slopes also are equal, then the lines will coincide and the system will have infinitely many solutions. It is given that the system has infinitely many solutions. So, the slopes must be equal. k/3 = 4/5. Multiply both sides by 3. k = 12/5. When k = 12/5, the system will have infinitely many solutions.If the system of linear equations2x + y z = 3x y z=α3x+3y+β z = 3has infinitely many solutions, then α+β αβ is equal to. Login. Study Materials. NCERT Solutions. NCERT Solutions For Class 12. NCERT Solutions For Class 12 Physics; NCERT Solutions For Class 12 Chemistry;Jan 3, 2024 · The lines intersect at a single point. Then the system has a unique solution corresponding to that point. The lines are parallel (and distinct) and so do not intersect. Then the system has no solution. The lines are identical. Then the system has infinitely many solutions—one for each point on the (common) line. Sep 17, 2022 · Theorem 1.5. 1: Rank and Solutions to a Homogeneous System. Let A be the m × n coefficient matrix corresponding to a homogeneous system of equations, and suppose A has rank r. Then, the solution to the corresponding system has n − r parameters. Consider our above Example 1.5. 2 in the context of this theorem. When you’re a renter, it can seem as though there is an infinite number of hoops to jump through just to get a foot in the door of an apartment you actually want to live in. You ha...A system of equations in 3 variables will have infinite solutions if the planes intersect in an entire line or in an entire plane. The latter case occurs if all three equations are equivalent and represent the same plane. Here is an example of the second case: x + y + z = 1. 2x + 2y + 2z = 2. 3x + 3y + 3z = 3. A question and answer platform for students and professionals. The web page provides a verified solution to a question about infinitely many solutions of a system of linear …Example 4: An Equation With Trig Functions With Infinitely Many Solutions. Consider the following equation with a trigonometric function: 2sin (x) = 1. sin (x) = ½. x = (12k + 1)π/6, (12k + 5)π/6 for any integer k. Since k can be any integer, there are infinitely many solutions for the equation. You can see the graph showing some of the ... We show that if V(|x|) has the following expansion: in which the constants are properly assumed, then ( ???) admits infinitely many non-radial solutions, whose energy can be made arbitrarily large. This is the first result for fractional Schrödinger equation. The s = 1 case corresponds to the known result in Wei-Yan \cite {WY}.For which values does the Matrix system have a unique solution, infinitely many solutions and no solution? 2 determinant of infinitely large matrix by decompositionTherefore, the given system of equations will have infinitely many solutions, if k = 7. Suggest Corrections. 2. Similar questions. Q. Find the value of k for which each of the following systems of equations have infinitely many solution:In this paper, we study the existence of infinitely many solutions for a fractional Kirchhoff–Schrödinger–Poisson system. Based on variational methods, especially the fountain theorem for the subcritical case and the symmetric mountain pass theorem established by Kajikiya for the critical case, we obtain infinitely many solutions for the …Apr 14, 2021 ... Welcome to this video, Test the consistency of the system of equations | No solution and infinitely many solutions | System of linear ...Can overdeterminend systems have infinitely many solutions? IF so, can someone point me to an example of one? linear-algebra; Share. Cite. Follow edited Jun 17, 2016 at 19:46. Tesla. 1,380 11 11 silver badges 38 38 bronze badges. asked Jun 17, 2016 at 19:28. Shammy Shammy.Question 4 (v) Find the values of p and q for the following pair of equations 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations has infinitely many solutions.Windows/Mac/Linux: The programming language that probably introduced more people to infinite loops than any other, Microsoft BASIC 6502 for the Commodore 64, is now available as a ...In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it: x. − 3y = 3 3x − 9y = 2. View Solution. Q2.Jacobs Solutions News: This is the News-site for the company Jacobs Solutions on Markets Insider Indices Commodities Currencies StocksHere, the given system of equations is consistent and has infinitely many solutions which form a two parameter family of solutions. Example 1.32. Test the consistency of the following system of linear equations. x − y + z = −9, 2x − y + z = 4, 3x − y + z = 6, 4x − y + 2z = 7. Solution. Here the number of unknowns is 3.Mar 25, 2020 ... The is an example of how to solve a system of equations using the method of elimination. In this example, there are infinitely many ...In this paper, the existence of infinitely many solutions for the partial discrete Kirchhoff-type problems involving p-Laplacian is proven by exploiting the ...Modified 9 years, 11 months ago. Viewed 2k times. 1. The question asks to find equation for which the system has infinitely many solutions. The system is: ⎧⎩⎨−cx + 3y + 2z = 8 x + z = 2 3x + 3y + az = b { − c x + 3 y + 2 z = 8 x + z = 2 3 x + 3 y + a z = b. How should I approach questions like this? The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value. View Solution. Q3. Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3Solutions to Linear Equations: A linear equation can have zero, one, or infinitely many solutions. A linear equation with no solutions simplifies to an untrue statement such as {eq}1 = 0 {/eq}.Therefore, the given system of equations will have infinitely many solutions, if k = 7. Suggest Corrections. 2. Similar questions. Q. Find the value of k for which each of the following systems of equations have infinitely many solution:Nov 16, 2022 · Speaking of which, let’s go ahead and work a couple of examples. We will start out with the two systems of equations that we looked at in the first section that gave the special cases of the solutions. Example 1 Use augmented matrices to solve each of the following systems. x −y = 6 −2x+2y = 1 x − y = 6 − 2 x + 2 y = 1. Find this value. (ii) Find c if the system of equations cx + 3y + 3 – c = 0, 12x + cy – c = 0 has infinitely many solutions? Q. Prove that there is a value of c (≠ 0) for which the system has infinitely many solutions. Find this value. 6x + 3y = c − 3.View Solution. Q 5. For what value of k, will the following pair of linear equations in two variable have infinitely many solutions? 2x+3y=4,(k+2)x+6y =3k+2. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:3 for what …In this paper we investigate a boundary value problem for a coupled nonlinear differential system of fractional order. Under appropriate hypotheses and by applying the critical point theorem, we obtain some new criteria to guarantee that the fractional differential system has infinitely many weak solutions. In addition, an …Example with infinitely many solutions: 3x + 3y = 3, 2x + 2y = 2, x + y = 1. Example with no solution: 3 x + 3 y + 3 z = 3, 2 x + 2 y + 2 z = 2, x + y + z = 1, x + y + z = 4. These results may be easier to understand by putting the augmented matrix of the coefficients of the system in row echelon form by using Gaussian elimination . Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (iv) x – 3 y – 7 = 0 and 3 x – 3 y 15 = 0 .View Solution. Q 5. For what value of k, will the following pair of linear equations in two variable have infinitely many solutions? 2x+3y=4,(k+2)x+6y =3k+2. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:3 for what …If slopes also are equal, then the lines will coincide and the system will have infinitely many solutions. It is given that the system has infinitely many solutions. So, the slopes must be equal. k/3 = 4/5. Multiply both sides by 3. k = 12/5. When k = 12/5, the system will have infinitely many solutions.There are 3 types of answers we can get when solving for a variable: x = a specific number (this is what we’ve been getting until now such as x = 5.3) x = all real numbers or infinitely many solutions (when we get x = x or when any number is equal to itself such as 3 = 3) No Solutions (when we end with a false statement like 1 = 5) When the two equations described parallel lines, there was no solution. We called that an inconsistent system. The same is true using substitution or elimination. If the equation at the end of substitution or elimination is a true statement, we have a consistent but dependent system and the system of equations has infinitely many solutions. The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1 has infinitely many solutions is _____ CBSE English Medium Class 10. Question Papers 992. Textbook Solutions 33593. MCQ Online Mock Tests 19. Important Solutions 5512.Aug 5, 2023 ... Infinite Many Solutions · Comments.Jan 3, 2024 · The lines intersect at a single point. Then the system has a unique solution corresponding to that point. The lines are parallel (and distinct) and so do not intersect. Then the system has no solution. The lines are identical. Then the system has infinitely many solutions—one for each point on the (common) line. Oct 11, 2011 ... Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that ...(ii) A single unique solution or (iii) Infinitely many solutions. Linear equation systems can be solved using various methods such as Graphical Method, Elimination Method, Cross Multiplication Method, Substitution Method, Matrix Method and Determinants Method. The set of all possible solutions is called the solution set.If multiple solutions exist, the system has infinitely many solutions; then we say that it is a consistent dependent system. If there is no solution for unknown factors, and this will happen if there are two or more equations that can’t be verified simultaneously, then we say that it’s an inconsistent system.Algebraic Equations with an Infinite Number of Solutions. You have seen that if an equation has no solution, you end up with a false statement instead of a value for x.It is possible to have an equation where any value for x will provide a solution to the equation. In the example below, notice how combining the terms [latex]5x[/latex] and [latex]-4x[/latex] on …Apr 2, 2013 ... Using row transformations, solva a 3x3 system of linear equations. This system has infinitely many solutions. Shows how to write the ...For which values does the Matrix system have a unique solution, infinitely many solutions and no solution? 2 determinant of infinitely large matrix by decompositionQuestion 2 The pair of equation x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has (A) a unique solution (B) exactly two solutions (C) infinitely many solutionsThe value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value. View Solution. Q3. Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3Q.42 of chapter 4, Find the value of m which the pair of linear equations 2x + 3y – 7 = 0 and (m – 1) x + (m + 1) y = (3m – 1) has infinitely many solutions.solutions. These are referred to as Consistent Systems of Equations, meaning that for a given system, there exists one solution set for the different variables in the system or infinitely many sets of solution. In other words, as long as we can find a solution for the system of equations, we refer to that system as being consistentDo you find yourself disagreeing with your client? Here are 11 ways to find a positive and effective solution. Maintaining a positive relationship with your clients is important fo...A question and answer platform for students and professionals. The web page provides a verified solution to a question about infinitely many solutions of a system of linear …Just as when we solved by substitution, this tells us we have a dependent system. There are infinitely many solutions. Solve for y in terms of z in the second equation. Solve the first equation for x in terms of z. Substitute y = 2 z + 2. y = 2 z + 2. Simplify. Simplify. Simplify. The system has infinitely many solutions (8 5,-42 5,-24 5) (8 5 ... Example 4: An Equation With Trig Functions With Infinitely Many Solutions. Consider the following equation with a trigonometric function: 2sin (x) = 1. sin (x) = ½. x = (12k + 1)π/6, (12k + 5)π/6 for any integer k. Since k can be any integer, there are infinitely many solutions for the equation. You can see the graph showing some of the ... There is one solution. There are infinitely many solutions. Thus, anytime you know there is more than one solution, you instantly know there are infinitely many solutions. NOTE: This only applies to straight lines. If you have any other kind of function, the rules for how many solutions there can be are different. Aug 20, 2015 ... For a complete list of Timely Math Tutor videos by course: www.timelymathtutor.com.For what value of k, will the following system of equations have infinitely many solutions? 2 x + 3 y = 4, (k + 2) x + 6 y = 3 k + 2. View Solution. Q5. The number of values of k for which the system of equations (k + 1) x + 8 y = 4 kQuestion: Find all values of and such that the system is 1. inconsistent; 2. consistent with exactly one solution; 3. consistent with infinitely many solutions. -axi – X2 = 3 1 -2x1 + 4x2 = 6b. Show transcribed image text. Here’s the best way to solve it. Aug 2, 2014 ... Share your videos with friends, family, and the world.Infinitely Many Solutions Equation When an equation has infinitely many equations, it means that if the variable in an equation was subsituted by a number, the equation would be correct or true, no matter what number/ value is subsituted. Infinitely many solutions; When there is no solution the equations are called "inconsistent". One or infinitely many solutions are called "consistent" Here is a diagram for 2 equations in 2 variables: Independent "Independent" means that each equation gives new information. Otherwise they are "Dependent". Also called "Linear Independence" …Tiger Global has backed the Indian industrial IoT startup Infinite Uptime in a Series B3 round of $18.85 million. Infinite Uptime, an Indian industrial IoT startup that offers pred...A matrix has infinitely many solutions when the following conditions are met: The matrix is a non-square matrix, meaning the number of rows is not equal to ...Modified 9 years, 11 months ago. Viewed 2k times. 1. The question asks to find equation for which the system has infinitely many solutions. The system is: ⎧⎩⎨−cx + 3y + 2z = 8 x + z = 2 3x + 3y + az = b { − c x + 3 y + 2 z = 8 x + z = 2 3 x + 3 y + a z = b. How should I approach questions like this? About the existence of infinitely many positive solutions, Coti-Zelati and Rabinowitz [13, 14] first proved the existence of arbitrary many number of bumps (hence infinitely many solutions) for when \(V\) is a periodic function in \(\mathbb {R}^N\), (see Sere for related work on Hamiltonian systems). As far as ...Spring is here and along with the good weather an infinite number of new TV shows and films are arriving this April. Once again, we’ll help you decide what to watch and how to spen...In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it: x. − 3y = 3 3x − 9y = 2. View Solution. Q2.For a pair of linear equations to have infinitely many solutions: `a_1/a_2 = b_1/b_2 = c_1/c_2` So, we need `k/12 = 3/k = (k - 3)/k` or `k/12 = 3/k` Which gives k 2 = 36, i.e., k = ± 6. Also, `3/k = (k - 3)/k` Gives 3k = k 2 – 3k, i.e., 6k = k 2, which means k = 0 or k = 6. Therefore, the value of k, that satisfies both the conditions, is k = 6. For this value, the …(C) infinitely many solutions (D) no solution 3. If a pair of linear equations is consistent, then the lines will be (A) parallel (B) always coincident (C) intersecting or coincident (D) always intersecting 4. The pair of equations y = 0 and y = –7 has (A) one solution (B) two solutions (C) infinitely many solutions (D) no solution 5.The first method to find the solution to the system of equations is the matrix method. The steps to be followed are given below: All the variables in the equations should be written in the appropriate order. ... B = 0, then the system is consistent and has infinitely many solutions. Note AX = 0 is known as the homogeneous system of linear equations, and …Nov 21, 2023 · In this lesson, learn about the types of solutions to systems of equations which are one solution, no solution, and infinitely many solutions with examples. Updated: 11/21/2023 Table of Contents
Infinitely solution, no solution, Pivoting, Pivot element, Transformation, The solution, General solution, Particular solution, Degree of freedom, Rank. ... Infinitely many solutions or no solution. 03. Systems of linear equations. Let's see this Linear algebra episode. Learn. Step by step.. Super mario rpg remake release date
If slopes also are equal, then the lines will coincide and the system will have infinitely many solutions. It is given that the system has infinitely many solutions. So, the slopes must be equal. k/3 = 4/5. Multiply both sides by 3. k = 12/5. When k = 12/5, the system will have infinitely many solutions. Conditions for Infinite and No Solutions. (a) If Δ = 0 and Δ1 = Δ2 = Δ3 = 0, then the system of the equation may or may not be consistent: (i) If the value of x, y and z in terms of t satisfy the third equation, then the system is said to be consistent and will have infinite solutions. (ii) If the values of x, y, and z don’t satisfy the ...For a pair of linear equations to have infinitely many solutions: From the given equtions, Put above values in equation (1) Posted by Safeer PP. View full answer Given pair of equations are. 2x + 3y = 7 and (k + 2) x – 3 (1 – k) y = 5k + 1. For a pair of linear equations to have infinitely many solutions: ...We're asked to find the number of solutions to this system of equations: − 6 x + 4 y = 2 3 x − 2 y = − 1. Interestingly, if we multiply the second equation by − 2 , we get the first equation: 3 x − 2 y = − 1 − 2 ( 3 x − 2 y) = − 2 ( − 1) − 6 x + 4 y = 2. In other words, the equations are equivalent and share the same graph. If the system of equations k x + 3 y − (k − 3) = 0, 12 x + k y − k = has infinitely many solutions, then k = Q. For which value of the given system of equations have infinitely many solution, ( k − 3 ) x + 3 y = k and k x + k y = 12Number of solutions to a system of equations graphically. Google Classroom. How many solutions does the system have? You can use the interactive graph below to find the answer. { x + 2 y = 2 2 x + 4 y = − 8. Dec 3, 2013 ... This example shows a solution with x arbitrary and a solution with y arbitrary.Jan 16, 2017 · For a given system of linear equations, there are three possibilities for the solution set of the system: No solution (inconsistent), a unique solution, or infinitely many solutions. Thus, for example, if we find two distinct solutions for a system, then it follows from the theorem that there are infinitely many solutions for the system. Jan 3, 2024 · The lines intersect at a single point. Then the system has a unique solution corresponding to that point. The lines are parallel (and distinct) and so do not intersect. Then the system has no solution. The lines are identical. Then the system has infinitely many solutions—one for each point on the (common) line. Download a PDF of the paper titled Infinitely many solutions for Schr\"{o}dinger-Newton equations, by Yeyao Hu and 2 other authors. Download PDF Abstract: We prove the existence of infinitely many non-radial positive solutions for the Schrödinger-Newton system $$Equations with infinitely many or no solutions Skills Linear equations can have one solution, no solutions, or infinitely many solutions. Learn all about these different …So let's take this down. So they say determine how many solutions exist for the system of equations. So you have 10x minus 2y is equal to 4, and 10x minus 2y is equal to 16. So just based on what we just talked about the x's and the y's are on the same side of the equation and the ratio is 10 to negative 2. Same ratio.We're asked to find the number of solutions to this system of equations: − 6 x + 4 y = 2 3 x − 2 y = − 1. Interestingly, if we multiply the second equation by − 2 , we get the first equation: 3 x − 2 y = − 1 − 2 ( 3 x − 2 y) = − 2 ( − 1) − 6 x + 4 y = 2. In other words, the equations are equivalent and share the same graph. Sep 17, 2022 · Preview Activity 1.2.1. Let's begin by considering some simple examples that will guide us in finding a more general approach. Give a description of the solution space to the linear system: x = 2 y = − 1. Give a description of the solution space to the linear system: − x + 2y − z = − 3 3y + z = − 1. 2z = 4. Apr 26, 2023 ... Abstract ... Here the function g(u) is periodic of mean zero, x \in R^n, r=|x|, \lambda _1 is the principal eigenvalue of \Delta on B. The problem ...Jan 19, 2019 ... Answer: real answer Sample Response: "You can start with any statement in the form a = a. Then add the same variable term to both sides, ...Dec 6, 2019 · Thus, in this case, if you have any solution at all, you already have infinitely many solutions, since you can add arbitrary multiples of the vector that's mapped to zero to the solution. Thus, a linear system of equations with a singular matrix has either zero or infinitely many solutions. For a pair of linear equations to have infinitely many solutions: `a_1/a_2 = b_1/b_2 = c_1/c_2` So, we need `k/12 = 3/k = (k - 3)/k` or `k/12 = 3/k` Which gives k 2 = 36, i.e., k = ± 6. Also, `3/k = (k - 3)/k` Gives 3k = k 2 – 3k, i.e., 6k = k 2, which means k = 0 or k = 6. Therefore, the value of k, that satisfies both the conditions, is k = 6. For this value, the ….
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