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3. In each of the following, one is given two vector spaces V and W and a transformation T: V→ W. Determine if T is linear. (a) V = W = M2x2 (R), T is defined by (b) V = R₂[X], W = R, T is defined by T(A) = AT. T(a+bX+cX²) = a +b+c+ 1. (c) V = R², W = M2x2 (R), T is defined by T(x) = x²x.

3. In each of the following, one is given two vector spaces V and W and a transformation T: V→ W. Determine if T is linear. (a) V = W = M2x2 (R), T is defined by (b) V = R₂[X], W = R, T is defined by T(A) = AT. T(a+bX+cX²) = a +b+c+ 1. (c) V = R², W = M2x2 (R), T is defined by T(x) = x²x.

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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SOLVE PARTS A, B, C

3. In each of the following, one is given two vector spaces V and W and a transformation T: V→ W. Determine if T is linear. (a) V = W = M2×2 (R), T is defined by (b) V = R₂[X], W = R, T is defined by T(A) = AT. T(a+bX+cX²) = a +b+c+ 1. (c) V = R², W = M2×2(R), T is defined by T(x) = x¹x.
Transcribed Image Text:3. In each of the following, one is given two vector spaces V and W and a transformation T: V→ W. Determine if T is linear. (a) V = W = M2×2 (R), T is defined by (b) V = R₂[X], W = R, T is defined by T(A) = AT. T(a+bX+cX²) = a +b+c+ 1. (c) V = R², W = M2×2(R), T is defined by T(x) = x¹x.
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