Let BV = {v1,v2} and BW = {w1,w2} be bases for vector spaces V and W, respectively. Let T : V → W be a linear transformation with the property that T(v1) = 3w1 − 4w2, T(v2) = −2w1 + 5w2. Find the matrix for T relative to BV and BW .

Let BV = {v1,v2} and BW = {w1,w2} be bases for vector spaces V and W, respectively. Let T : V → W be a linear transformation with the property that T(v1) = 3w1 − 4w2, T(v2) = −2w1 + 5w2. Find the matrix for T relative to BV and BW .

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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Question

Let BV = {v1,v2} and BW = {w1,w2} be bases for vector spaces V and W, respectively. Let T : V → W be a linear transformation with the property that

T(v1) = 3w1 − 4w2,

T(v2) = −2w1 + 5w2.

Find the matrix for T relative to BV and BW .

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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