Let A be a 3 x 3 matrix, and let S = {v1,V2, V3} be a linearly independent set in R suchthatAv = V1, Av2 = -V2, Av3 = 0.%3D(a) Let w = v1+v2 + V3. Show that v1, V2 and v3 are all in Span{w, Aw, A?w}.

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Let A be a 3 x 3 matrix, and let S = {v1, V2, V3} be a linearly independent set in R such %3D that Avi = V1, Av2 = -V2, Av3 = 0. (a) Let w =vı+ v2 + V3. Show that v1, V2 and v3 are all in Span{w, Aw, A?w}.

Let A be a 3 x 3 matrix, and let S = {v1, V2, V3} be a linearly independent set in R such %3D that Avi = V1, Av2 = -V2, Av3 = 0. (a) Let w =vı+ v2 + V3. Show that v1, V2 and v3 are all in Span{w, Aw, A?w}.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section: Chapter Questions

Problem 17RQ

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Question

Let A be a 3 x 3 matrix, and let S = {v1,V2, V3} be a linearly independent set in R such
that
Av = V1, Av2 = -V2, Av3 = 0.
%3D
(a) Let w = v1+v2 + V3. Show that v1, V2 and v3 are all in Span{w, Aw, A?w}.

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