Let I2 € M₂(K) be the 2 × 2 identity matrix, where K is a field. For any A € M₂(K), letV₁ = 12, V₂ = A, V3 = A²and regard them as elements of V = M₂(K) as a vector space.[ 1(i) Show that v₁, V2, V3 are linearly dependent as elements of V.Let K = R and A

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Let I2 € M₂(K) be the 2 × 2 identity matrix, where K is a field. For any A € M₂(K), let V₁ = I2, V₂ = A, and regard them as elements of V = M₂(K) as a vector space. = A² Let K = R and A V3 = 61 (i) Show that V₁, V2, V3 are linearly dependent as elements of V.

Let I2 € M₂(K) be the 2 × 2 identity matrix, where K is a field. For any A € M₂(K), let V₁ = I2, V₂ = A, and regard them as elements of V = M₂(K) as a vector space. = A² Let K = R and A V3 = 61 (i) Show that V₁, V2, V3 are linearly dependent as elements of V.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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Question

Let I2 € M₂(K) be the 2 × 2 identity matrix, where K is a field. For any A € M₂(K), let
V₁ = 12, V₂ = A, V3 = A²
and regard them as elements of V = M₂(K) as a vector space.
[ 1
(i) Show that v₁, V2, V3 are linearly dependent as elements of V.
Let K = R and A

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