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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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