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а 0 a² – 2 | A = 1 1 -1 а а-1 (a) For what values of a does the system Ax = b have a unique solution for all b? (b) State Cramer's rule and use it to solve the system when a = 1 and b" (4, 2, 4)- (c) Does A have an inverse when a = = -1?

а 0 a² – 2 | A = 1 1 -1 а а-1 (a) For what values of a does the system Ax = b have a unique solution for all b? (b) State Cramer's rule and use it to solve the system when a = 1 and b" (4, 2, 4)- (c) Does A have an inverse when a = = -1?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 29E
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Part d

0 a? – 2 a - A = 0 1 1 -1 a - 1 (a) For what values of a does the system Ax = b have a unique solution for all 6? (b) State Cramer's rule and use it to solve the system when a = 1 and b" = (4, 2, 4). %3D (c) Does A have an inverse when a = –1? (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three vectors u = x – y, v = x – z, and w = y – z also linearly independent? Explain. |
Transcribed Image Text:0 a? – 2 a - A = 0 1 1 -1 a - 1 (a) For what values of a does the system Ax = b have a unique solution for all 6? (b) State Cramer's rule and use it to solve the system when a = 1 and b" = (4, 2, 4). %3D (c) Does A have an inverse when a = –1? (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three vectors u = x – y, v = x – z, and w = y – z also linearly independent? Explain. |
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