- #1
Robb
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Homework Statement
Let A and B be matrices for which the product AB is defined. Show that the column space of AB is contained in the column space of A.
Homework Equations
perform one elementary row operation to matrix A to obtain matrix B.
The Attempt at a Solution
1 2
3 4 = A
2 4
6 8 = 2A = B
14 20
30 44 = AB
Obviously the colsp(A) = colsp(B) given that B is a linear combination of A, but I don't see how colsp(AB) = colsp(A) and is therefore contained in A. Please advise.
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