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tatianaiistb
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Homework Statement
If VΩW contains only the zero vector, then dim(V+W)+dim(VΩW) = dim(v) + dim(W) becomes dim(V+W) = dim(v) + dim(W). Check this when V is the row space of A, W is the nullspace of A, and the matrix A is mxn of rank r. What are the dimensions?
Homework Equations
dim(V+W)+dim(VΩW) = dim(v) + dim(W)
The Attempt at a Solution
I don't even know how to start this problem.
I do know that dim(V+W) + dim (VΩW) = rank of [A B] + nullity of [A B]
Can anyone help? Thanks!