Exercise 9.2.7 Determine whether each of the following sets of matrices is linearly independent. If it is linearly dependent, write one matrix as a linear combination of the other matrices in the set. (a) {[13] [3 2 -2 -3 4 0 2 1 (b) { [ 8 ] [ 8 ] [ ¦ 8 ] [ 8 ])} 0 1 0
Exercise 9.2.7 Determine whether each of the following sets of matrices is linearly independent. If it is linearly dependent, write one matrix as a linear combination of the other matrices in the set. (a) {[13] [3 2 -2 -3 4 0 2 1 (b) { [ 8 ] [ 8 ] [ ¦ 8 ] [ 8 ])} 0 1 0
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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![**Exercise 9.2.7** Determine whether each of the following sets of matrices is linearly independent. If it is linearly dependent, write one matrix as a linear combination of the other matrices in the set.
(a)
\[
\left\{\begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} -7 & 2 \\ -2 & -3 \end{bmatrix}, \begin{bmatrix} 4 & 0 \\ 1 & 2 \end{bmatrix}\right\}
\]
(b)
\[
\left\{\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 1 & 1 \end{bmatrix}\right\}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dabe4e8-4d41-42d6-aeb9-4a7fca8c4b16%2Fa23fe840-4d2f-4dac-a68e-706e99cdf928%2Ffvno3r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 9.2.7** Determine whether each of the following sets of matrices is linearly independent. If it is linearly dependent, write one matrix as a linear combination of the other matrices in the set.
(a)
\[
\left\{\begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} -7 & 2 \\ -2 & -3 \end{bmatrix}, \begin{bmatrix} 4 & 0 \\ 1 & 2 \end{bmatrix}\right\}
\]
(b)
\[
\left\{\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 0 & 0 \\ 1 & 1 \end{bmatrix}\right\}
\]
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