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

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

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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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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