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1. The map T : Mat2,2(R) → Mat2,2(R) given by a +c d a b T c d а — d

1. The map T : Mat2,2(R) → Mat2,2(R) given by a +c d a b T c d а — d

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 : Mat2,2(R) → Mat2,2(R) given by r(: ) - (**" .-) a b T а +с а — d d 2. The map T : Mat2,2(R) → Mat2,2(R) given by a + c 1 a T с а 1 а — d 3. The map T : Matn.n(R) → Mat,n.n(R) given by T(A) = A · B – B · A where B E Mat,.n (R) is fixed. 3,n 4. The map T : Mat,.n (R) → R given by T(A) = Tr(A · B – B · A) where Be Mat„,n(IR) is fixed. 5. The map T : Fun(R, R) → Fun(R, R) given by T(f(t)) = f(t²). 6. The map T : Fun(R, R) → Fun(IR, IR) given by T(F (t)) = (f(t))².
Transcribed Image Text:For each of the following, determine (with argument) whether the given function T is linear. 1. The map T : Mat2,2(R) → Mat2,2(R) given by r(: ) - (**" .-) a b T а +с а — d d 2. The map T : Mat2,2(R) → Mat2,2(R) given by a + c 1 a T с а 1 а — d 3. The map T : Matn.n(R) → Mat,n.n(R) given by T(A) = A · B – B · A where B E Mat,.n (R) is fixed. 3,n 4. The map T : Mat,.n (R) → R given by T(A) = Tr(A · B – B · A) where Be Mat„,n(IR) is fixed. 5. The map T : Fun(R, R) → Fun(R, R) given by T(f(t)) = f(t²). 6. The map T : Fun(R, R) → Fun(IR, IR) given by T(F (t)) = (f(t))².
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