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If W, and W2 are finite - dimensional subspaces of a vector space V, then W + W2 is finite – demesional and dim W, + dim W2 = dim (W1 n W2) + dim (W1 + W2).

If W, and W2 are finite - dimensional subspaces of a vector space V, then W + W2 is finite – demesional and dim W, + dim W2 = dim (W1 n W2) + dim (W1 + W2).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 43EQ
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.If W1 and W2 are finite - dimensional subspaces of a vector space V, then W + W2 is finite - demesional and dim W1 + dim W2 dim ( W n W2) + dim (W1 + W2).
Transcribed Image Text:.If W1 and W2 are finite - dimensional subspaces of a vector space V, then W + W2 is finite - demesional and dim W1 + dim W2 dim ( W n W2) + dim (W1 + W2).
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