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3. Let V and W be subspaces of M2×3 of dimensions 3 and 4, respectively. Prove that there exists a non-zero matrix A Є M2×3 such that A = VW. You might find the following dimension formula useful: dim(V +W) = dim(V) + dim(W) – dim(VW).

3. Let V and W be subspaces of M2×3 of dimensions 3 and 4, respectively. Prove that there exists a non-zero matrix A Є M2×3 such that A = VW. You might find the following dimension formula useful: dim(V +W) = dim(V) + dim(W) – dim(VW).

Elementary Linear Algebra (MindTap Course List)
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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3. Let V and W be subspaces of M2×3 of dimensions 3 and 4, respectively. Prove that there exists a non-zero matrix A Є M2×3 such that A = VW. You might find the following dimension formula useful: dim(V +W) = dim(V) + dim(W) – dim(VW).
Transcribed Image Text:3. Let V and W be subspaces of M2×3 of dimensions 3 and 4, respectively. Prove that there exists a non-zero matrix A Є M2×3 such that A = VW. You might find the following dimension formula useful: dim(V +W) = dim(V) + dim(W) – dim(VW).
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