Exercise 9.2.4 (a) Write A = 13 0 0 as a linear combination of (49). 88 89 (80) (b) Show that the above set of four matrices is a spanning set for M2,2, the vector space of all 2 × 2- matrices.
Exercise 9.2.4 (a) Write A = 13 0 0 as a linear combination of (49). 88 89 (80) (b) Show that the above set of four matrices is a spanning set for M2,2, the vector space of all 2 × 2- matrices.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Exercise 9.2.4**
(a) Write \( A = \begin{bmatrix} 1 & 3 \\ 0 & 0 \end{bmatrix} \) as a linear combination of
\[
\left\{ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 1 \end{bmatrix} \right\}.
\]
(b) Show that the above set of four matrices is a spanning set for \( M_{2,2} \), the vector space of all \( 2 \times 2 \)-matrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dabe4e8-4d41-42d6-aeb9-4a7fca8c4b16%2F2ba20aba-6856-4eb9-8edd-da264f45d336%2Ffst1ld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 9.2.4**
(a) Write \( A = \begin{bmatrix} 1 & 3 \\ 0 & 0 \end{bmatrix} \) as a linear combination of
\[
\left\{ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 1 \end{bmatrix} \right\}.
\]
(b) Show that the above set of four matrices is a spanning set for \( M_{2,2} \), the vector space of all \( 2 \times 2 \)-matrices.
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