5) be a subspace of M₂x2(R). Let S = a) Determine a basis for S. Y a1 a2 a3 a4 | a₁ + a₂-2a3=0=a3-5a4} b) Compute the dimension of S. c) Let dim(S) = m, construct an isomorphism between S and Rm (i.e. write a formula for a linear transformation which is an isomorphism).
5) be a subspace of M₂x2(R). Let S = a) Determine a basis for S. Y a1 a2 a3 a4 | a₁ + a₂-2a3=0=a3-5a4} b) Compute the dimension of S. c) Let dim(S) = m, construct an isomorphism between S and Rm (i.e. write a formula for a linear transformation which is an isomorphism).
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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Transcribed Image Text:5)
be a subspace of M₂x2 (R).
Let S = {[
a1
a3
a2
a4
| a₁ + a2-2a3 = 0 = a3-5a4}
a) Determine a basis for S.
b) Compute the dimension of S.
c) Let dim(S) = m, construct an isomorphism between S and Rm (i.e. write
a formula for a linear transformation which is an isomorphism).
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