2. Suppose the matrix, A, is the augmented matrix of a system of equations.1-2k 76-8a) Write out the corresponding system of equations using variables x and y.b) Find the value of k for which the system is inconsistent (has no solution).

Given matrix: This is the augmented matrix for the system of equations i.e.(a): We have to write…

Answered: 2. Suppose the matrix, A, is the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Assume that the following augmented matrix represents a system of linear equations. -1 -8 2 -1 -2 -20 -8 -1 -1 -14-3 What kind of solution does this system have? (A) infinitely many solutions with 2 arbitrary (free) parameters (B) 3 solutions (C) infinitely many solutions with 1 arbitrary (free) parameter (D) 2 solutions (E) unique solution (F) infinitely many solutions with 4 arbitrary (free) parameters (G) infinitely many solutions with 3 arbitrary (free) parameters (H) no solution A O B O E G H
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2. Let a, b and c be real numbers. Consider the system of linear equations that has augmented matrix: 1 0 0 0 3 1 06+2 2 2 2 - 3 b a 0 0 00c² c²-1 c+1 (a) For which values of a, b, and c is the system inconsistent? Justify. (b) For which values of a, b, and c is the system consistent with unique solution? Justify. (c) For which values of a, b, and c is the system consistent with infinitely many solutions? Justify.
2. A linear system is described by the following equations. 2a 2b + c a + 3b - 2c = 1 3a - b - c = 2 = (a) (b) -3 From the given linear equations, identify the matrices A, x and b such the the linear system can be expressed as a matrix equation. Does this system have any unique solution? Explain. Evaluate the upper triangular matrix U. Note that you have to show the row multipliers mij for each step as necessary. (d) Using the upper triangular matrix found in the previous question, compute the solution of the given linear system by Gaussian elimination method.
I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3
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Suppose that a system of linear equations has augmented matrix 5 — -1 0 0 1 2 2 1 0 1 3 1 3 1 How many variables does the system have?
6. Write the system in matrix form, then find a general solution of the system x1 + 4.x2 = x1 – 2x2 -

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2. Suppose the matrix, A, is the augmented matrix of a system of equations. k 7 -2 6-8 a) Write out the corresponding system of equations using variables x and y. b) Find the value of k for which the system is inconsistent (has no solution).