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-5a + 5b+ 6c -3b + 2c U = E M2 (R) a, b, c ER 3a + 2b - 4c 4a + 5c

-5a + 5b+ 6c -3b + 2c U = E M2 (R) a, b, c ER 3a + 2b - 4c 4a + 5c

Advanced Engineering Mathematics
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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(a) Consider the subset U of M2 (R) given by -5a + 5b + 6c -3b + 2c U = E M2 (R) a, b, c ER 3a + 2b – 4c 4а + 5c Show that U is a subspace of M2 (R) by exhibiting it as the span of a set of matrices in M2 (R): U = Span (b) The set B = -6 is a basis for a subspace W of M2 (R). Use this basis to answer parts (i) and (ii) below. 94 (i) The matrix A = 65 97 38 belongs to W. Find the coordinate vector [A]B. [A]B (ii) Let CE W. Suppose [C]B = -3 Then C =
Transcribed Image Text:(a) Consider the subset U of M2 (R) given by -5a + 5b + 6c -3b + 2c U = E M2 (R) a, b, c ER 3a + 2b – 4c 4а + 5c Show that U is a subspace of M2 (R) by exhibiting it as the span of a set of matrices in M2 (R): U = Span (b) The set B = -6 is a basis for a subspace W of M2 (R). Use this basis to answer parts (i) and (ii) below. 94 (i) The matrix A = 65 97 38 belongs to W. Find the coordinate vector [A]B. [A]B (ii) Let CE W. Suppose [C]B = -3 Then C =
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