6. (4 pts) If B is an k x m matrix and A is an m x n matrix, prove that nullity(BA) ? nullity(A), rank(BA) ? rank(A).
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Step 1
Since BA is an k x m matrix, we can use the fact that k > n to conclude that BA has at least k columns. Since each column in BA corresponds to a distinct value in A, it follows that BA has at least k + 1 columns. Therefore, nullity(BA) > nullity(A). Show more…
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