5) be a subspace of M2x2 (R). Let S = a1 a2 a3 a4 | a₁ + a2-2a3=0=a3-5a4} + a₂- 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).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
icon
Related questions
Question
100%

any help would be nice thanks!!

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).
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).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning