(d) Show that T' is an isomorphism. (e) Find the matrix representation of T with respect to the standard bases of M22 and R4.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
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Need help with parts (d) and (e). Thank you :)

8. (a) Write down the standard bases for M22 and R4.
(b) From your answer to (a), explain why M22 and R' are isomorphic.
Consider the function T: M22 → R' defined by
().
a) = (4, b, a, c).
T
d
(c) Show that T is a linear transformation.
(d) Show that T is an isomorphism.
(e) Find the matrix representation of T with respect to the standard bases of M22 and R4.
Transcribed Image Text:8. (a) Write down the standard bases for M22 and R4. (b) From your answer to (a), explain why M22 and R' are isomorphic. Consider the function T: M22 → R' defined by (). a) = (4, b, a, c). T d (c) Show that T is a linear transformation. (d) Show that T is an isomorphism. (e) Find the matrix representation of T with respect to the standard bases of M22 and R4.
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