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1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k For which values of k will the system have: infinitely many solutions? no solution? one unique solution? 2. Find all the solutions to the system below describing your solution set in vector notation using free variables. T1 - 3x2 + 2x3+ 2x4 + 2x5 = 1 -x1 + 3x2 + 4x4 - 6x5 1 2x1 - 6x2 + 3x3 + 6x4 + x5 = 1 : and B= 3. Given the matrices A = show that A and B have the same eigenvalues. 47 1 8 4. Let A = 1 2x 2x x (a) Find the determinant of A. (b) For what values of x is the matrix A nonsingular?

1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k For which values of k will the system have: infinitely many solutions? no solution? one unique solution? 2. Find all the solutions to the system below describing your solution set in vector notation using free variables. T1 - 3x2 + 2x3+ 2x4 + 2x5 = 1 -x1 + 3x2 + 4x4 - 6x5 1 2x1 - 6x2 + 3x3 + 6x4 + x5 = 1 : and B= 3. Given the matrices A = show that A and B have the same eigenvalues. 47 1 8 4. Let A = 1 2x 2x x (a) Find the determinant of A. (b) For what values of x is the matrix A nonsingular?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 44EQ
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1. Consider the following system of linear equations: X1+ kx2 = 2 kæ1 + x2 + x3 = 1 x1 + x2 + x3 = k For which values of k will the system have: infinitely many solutions? no solution? one unique solution? 2. Find all the solutions to the system below describing your solution set in vector notation using free variables. x1 – 3x2 + 2x3 + 2x4 + 2x5 =1 -x1+ 3x2 + 4x4 – 6x5 = 1 2.x1 – 6x2 + 3x3 + 6x4 + x5 = 1 3. Given the matrices A = and B = show that A and B have the same a eigenvalues. 0 4 4. Let A = 2x 1 1 8. (a) Find the determinant of A. (b) For what values of r is the matrix A nonsingular?
Transcribed Image Text:1. Consider the following system of linear equations: X1+ kx2 = 2 kæ1 + x2 + x3 = 1 x1 + x2 + x3 = k For which values of k will the system have: infinitely many solutions? no solution? one unique solution? 2. Find all the solutions to the system below describing your solution set in vector notation using free variables. x1 – 3x2 + 2x3 + 2x4 + 2x5 =1 -x1+ 3x2 + 4x4 – 6x5 = 1 2.x1 – 6x2 + 3x3 + 6x4 + x5 = 1 3. Given the matrices A = and B = show that A and B have the same a eigenvalues. 0 4 4. Let A = 2x 1 1 8. (a) Find the determinant of A. (b) For what values of r is the matrix A nonsingular?
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