Let A Be An Arbitrary M X N Matrix And Let B Be An Arbitrary N X P Matrix Show T

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Let A be an arbitrary m x n matrix, and let B be an arbitrary n x p matrix.

a. Show that any vector x that is in the column space of AB is also in the column space of A.

b. Is it also true that any vector x that is in the column space of AB is also in the column space ofB? Why or why not?

c. Is it also true that any vector x that is in the column space of A is also in the column space ofAB? Why or why not?

 
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