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For each of the following, determine (with argument) whether the given function T is linear. 1. The map T : Mat,2(R) → Mat2,2(R) given by a+c a b T c d d a - d 2. The map T : Mat2,2(R) → Mat2,2(R) given by "(: ) = (":" .'-) a b T a +c a –d, 1 3. The map T : Mat,,m(R) → Mat,,n (R) given by T(A) = A · B – B · A where Be Mat,n,n(R) is fixed. %3D

For each of the following, determine (with argument) whether the given function T is linear. 1. The map T : Mat,2(R) → Mat2,2(R) given by a+c a b T c d d a - d 2. The map T : Mat2,2(R) → Mat2,2(R) given by "(: ) = (":" .'-) a b T a +c a –d, 1 3. The map T : Mat,,m(R) → Mat,,n (R) given by T(A) = A · B – B · A where Be Mat,n,n(R) is fixed. %3D

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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For each of the following, determine (with argument) whether the given function T is linear. 1. The map T : Mat,2(R) → Mat2,2(R) given by a+c a b T c d d a - d 2. The map T : Mat2,2(R) → Mat2,2(R) given by "(: ) = (":" .'-) a b T a +c a –d, ). 1 3. The map T : Mat,,m(R) → Mat,,n (R) given by T(A) = A · B – B · A where Be Mat,n,n(R) is fixed.
Transcribed Image Text:For each of the following, determine (with argument) whether the given function T is linear. 1. The map T : Mat,2(R) → Mat2,2(R) given by a+c a b T c d d a - d 2. The map T : Mat2,2(R) → Mat2,2(R) given by "(: ) = (":" .'-) a b T a +c a –d, ). 1 3. The map T : Mat,,m(R) → Mat,,n (R) given by T(A) = A · B – B · A where Be Mat,n,n(R) is fixed.
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