Answer a and b ->Let T: R³ R3 be the linear transformation defined by T(x₁, x2, x3) = (x₁ + 2x₂ + x3,-X2, X1 + 4x3). Let a be the standard basis, and let ß = {(1, 0, 0), (1, 1,0), (1, 1, 1)) for R³. Findthe associated matrix of T with respect to a and the associated matrix of T with respect to ß.Are they similar?b) (i) Show that the differential operator D: P3 (R) → P₂ (R) defined by D(p(x)) = p'(x) is Linear.Also, find the kernel and image of the differential operator D.(ii) Let T: R³-R² be the linear transformation defined by T(x, y, z)=(x-y, 2z). Find thekernel and image of T.

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Let T: R³ R3 be the linear transformation defined by T(x₁, x2, x3) = (x₁ + 2x₂ + x3, -X2, X1 + 4x3). Let a be the standard basis, and let ß= {(1, 0, 0), (1, 1,0), (1, 1, 1)) for R³. Find the associated matrix of T with respect to a and the associated matrix of T with respect to B. Are they similar? D. (DY R(R) defined by (n(x)) = n'(x) is Linear.

Let T: R³ R3 be the linear transformation defined by T(x₁, x2, x3) = (x₁ + 2x₂ + x3, -X2, X1 + 4x3). Let a be the standard basis, and let ß= {(1, 0, 0), (1, 1,0), (1, 1, 1)) for R³. Find the associated matrix of T with respect to a and the associated matrix of T with respect to B. Are they similar? D. (DY R(R) defined by (n(x)) = n'(x) is Linear.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 23EQ

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