Let E= {e,, ez, ez} be the standard basis for R, B = {b,, b,, b3} be a basis for a vector space V, and T:R → V be a linear transformation with the property thatT(X1, X2, X3) = (X3- X2) b1 - (X1 + X3) b2 * (*1 - X2) b3.a. Compute T(e,), T(e2), and T(e3).b. Compute [T (e1)]B• [T(e2)]B• and [T(e3)]s-c. Find the matrix for T relative to E and B.a. T(e,) =T(e2)=|and T(e3) =. [T(e1) ]s=O [T(*:) ]3=], and [T(es)]a=Ob.c. The matrix for T relative to E and B is.

Let E= {e,, e2, e3} be the standard basis for R°, B= (b, , b2, b3} be a basis for a vector space V, and T:R° → V be a linear transformation with the property that (x1, X2, ×3) = (x3 - ×2) b, - (×1 + X3) b2 * (x1 - X2) b3. a. Compute T(e,), T(@2), and T(@3). p. Compute [T(e1)]B• [T(@2)]8• and [T(®3)]B• . Find the matrix for T relative to E and B. .. a. T(e,) =], T(e2) =D, and T(e3) = [ ["(•) ]==D•["(*2) ]e-0, and [T(*3) ]e =D c. The matrix for T relative to E and B is.

Let E= {e,, e2, e3} be the standard basis for R°, B= (b, , b2, b3} be a basis for a vector space V, and T:R° → V be a linear transformation with the property that (x1, X2, ×3) = (x3 - ×2) b, - (×1 + X3) b2 * (x1 - X2) b3. a. Compute T(e,), T(@2), and T(@3). p. Compute [T(e1)]B• [T(@2)]8• and [T(®3)]B• . Find the matrix for T relative to E and B. .. a. T(e,) =], T(e2) =D, and T(e3) = [ ["(•) ]==D•["(2) ]e-0, and [T(3) ]e =D c. The matrix for T relative to E and B is.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 54EQ

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