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5. (a) Consider T = LA: R³ - where A is the matrix A = R¹, T(x) = Ax 1 0 0 0 1 0 000 000 (In the notation of the lecture notes, T = LA, the linear map defined by matrix multilplication by A on the left.) Show that the rank and nullity of T are 2 & 1 and find a basis for the image im(T) and the kernel ker(T).

5. (a) Consider T = LA: R³ - where A is the matrix A = R¹, T(x) = Ax 1 0 0 0 1 0 000 000 (In the notation of the lecture notes, T = LA, the linear map defined by matrix multilplication by A on the left.) Show that the rank and nullity of T are 2 & 1 and find a basis for the image im(T) and the kernel ker(T).

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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[EX4 Q5] A question about matrix :)

5. (a) Consider T = LÃ: R³ → R¹, T(x) = Ax where A is the matrix A = 100 010 00 000 = I LA, the linear map defined by T (In the notation of the lecture notes, T matrix multilplication by A on the left.) Show that the rank and nullity of T are 2 & 1 and find a basis for the image im(T) and the kernel ker(T). T
Transcribed Image Text:5. (a) Consider T = LÃ: R³ → R¹, T(x) = Ax where A is the matrix A = 100 010 00 000 = I LA, the linear map defined by T (In the notation of the lecture notes, T matrix multilplication by A on the left.) Show that the rank and nullity of T are 2 & 1 and find a basis for the image im(T) and the kernel ker(T). T
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