Tanner W.

asked • 05/16/16

When multiplying two matrices does A(B + C) = AB + AC?

When multiplying two matrices does A(B + C) = AB + AC?
 
yes or no

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Michael J. answered • 05/16/16

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Only when you compute dot multipication.  If you compute the cross multiplication, then you will get a different result.
 
Dot multiplication consists of multiplying matrices element by element.  Cross multiplication consists of a combination of multiplying by rows and columns, then adding the elements.  The products between dot and cross multiplication will differ.
 
 
A.(B + C) ≠ A×(B + C)
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Arturo O.

But the question is about matrix multiplication, not vector multiplication.  Your statement is correct if you are answering a question about vector multiplication.
 
A.(B+C) is the dot product of vector A with vector (B+C), which is a scalar; whereas Ax(B+C) is the cross product of vector A with vector (B+C), which is another vector.  Since the question is about matrix multiplication, then
 
A(B+C) = AB + BC with the only condition that AB and AC be possible. i.e. if A is an mxn matrix, then both B and C must be nxq matrices, resulting in an mxq matrix for the product matrix.  Otherwise the product is not even defined.
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05/23/16

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