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2. (a) A linear map T : M2,2(R) P2 (R) is defined by a b ( 2) = (a + b)x? + (a +b – d+2c)x - (c+d). Is T is an isomorphism? Justify your answer. (b) Let T : R3 R3 be a linear map defined by T((x,y,z)) = (x+ y- z, z – y,7x). Is T invertable? Justify your answer.

2. (a) A linear map T : M2,2(R) P2 (R) is defined by a b ( 2) = (a + b)x? + (a +b – d+2c)x - (c+d). Is T is an isomorphism? Justify your answer. (b) Let T : R3 R3 be a linear map defined by T((x,y,z)) = (x+ y- z, z – y,7x). Is T invertable? Justify your answer.

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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2. (a) A linear map T : M22(R) → P2(R) is defined by ( a) = (a +b)x² + (a + b – d +2c)x -(c+d). T Is T is an isomorphism? Justify your answer. (b) Let T : R3 → R³ be a linear map defined by T((x,y,z)) = (x + y- z,z – y,7x). Is T invertable? Justify your answer.
Transcribed Image Text:2. (a) A linear map T : M22(R) → P2(R) is defined by ( a) = (a +b)x² + (a + b – d +2c)x -(c+d). T Is T is an isomorphism? Justify your answer. (b) Let T : R3 → R³ be a linear map defined by T((x,y,z)) = (x + y- z,z – y,7x). Is T invertable? Justify your answer.
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