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State with reasons whether each of the following maps S : Mat2.2(R) → Mat2.2(R) is linear. For (6 9)- (C ) those maps that are linear: (i) find their matrix with respect to the basis (* :) (C )> ; and (ii) find their rank and nullity. (a) S(A) = A² (b) S(A) = CA, where C = %3D 4

State with reasons whether each of the following maps S : Mat2.2(R) → Mat2.2(R) is linear. For (6 9)- (C ) those maps that are linear: (i) find their matrix with respect to the basis (* :) (C )> ; and (ii) find their rank and nullity. (a) S(A) = A² (b) S(A) = CA, where C = %3D 4

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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State with reasons whether each of the following maps S : Mat2.2(R) → Mat2.2(R) is linear. For 1 C ). 1 those maps that are linear: (i) find their matrix with respect to the basis 0 0 (* :)- (C ) and (ii) find their rank and nullity. 1 1 1 (a) S(A) = A? (b) S(A) = CA, where C = 2 4
Transcribed Image Text:State with reasons whether each of the following maps S : Mat2.2(R) → Mat2.2(R) is linear. For 1 C ). 1 those maps that are linear: (i) find their matrix with respect to the basis 0 0 (* :)- (C ) and (ii) find their rank and nullity. 1 1 1 (a) S(A) = A? (b) S(A) = CA, where C = 2 4
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