[EX4 Q5] A question about matrix :) 5. (a) ConsiderT = LÃ: R³ → R¹, T(x) = Axwhere A is the matrixA=10001000000=ILA, the linear map defined byT(In the notation of the lecture notes, Tmatrix 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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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).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 55EQ

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