1. Consider the following matrices A₁, A2, A3, B in the vector space M2,2 of 2 × 2 matrices, 1 -1 1 2 7 ^ = [ 2 ]] - 4 = [ †; } } ] - ^ = [ 3 ] = [¹/² 77²] A₁ A3 B 15/2 2 22 1 1 0 9 Express B as a linear combination of A1, A2, A3 if B € span{A₁, A2, A3}, otherwise show why B span{A1, A2, A3}.
1. Consider the following matrices A₁, A2, A3, B in the vector space M2,2 of 2 × 2 matrices, 1 -1 1 2 7 ^ = [ 2 ]] - 4 = [ †; } } ] - ^ = [ 3 ] = [¹/² 77²] A₁ A3 B 15/2 2 22 1 1 0 9 Express B as a linear combination of A1, A2, A3 if B € span{A₁, A2, A3}, otherwise show why B span{A1, A2, A3}.
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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![1. Consider the following matrices A₁, A2, A3, B in the vector space M2,2 of 2 × 2 matrices,
1
2
^ = []}]} 4-[+]}^^= [7] 8 [15/2 77/2]
1]
A₁
B
2
22
1
0 1
9
A₂
A3
=
Express B as a linear combination of A1, A2, A3 if B € span{A₁, A2, A3}, otherwise
show why B span{A1, A2, A3}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F882ce437-6984-48a2-b1c1-0c70a26630a5%2Ffdc7e85c-806d-4b7a-9a2b-6bfbbf73efb3%2Fxq1gsr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the following matrices A₁, A2, A3, B in the vector space M2,2 of 2 × 2 matrices,
1
2
^ = []}]} 4-[+]}^^= [7] 8 [15/2 77/2]
1]
A₁
B
2
22
1
0 1
9
A₂
A3
=
Express B as a linear combination of A1, A2, A3 if B € span{A₁, A2, A3}, otherwise
show why B span{A1, A2, A3}.
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