Show that matrix AB has its row and column vectors in A and B

  • Thread starter jheld
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  • #1
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Homework Statement


Given matrices A and B, show that the row vectors of AB are in the row space of B an the column vectors of AB are in the column space of A


Homework Equations


Just matrix multiplication, reduced row echelon form, and leading one's for row and columns


The Attempt at a Solution


I am unsure if I need to find the two separate matrices, or if this is just a general problem.
I understand what they are asking, but I am unsure of how to find the right matrices, and what it means to be "in" the row and column vectors. I think it means that they are in the correct rows and columns from the respective single matrices A and B.
 

Answers and Replies

  • #2
Dick
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It means that a row of AB is a linear combination of rows of B and a column of AB is a linear combination of columns of A. All you need is the definition of matrix multiplication, A_{ij}*B_{jk}=(AB)_{ik}.
 

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