Matrix (mathematics)

For the square matrix section, see square matrix.

Adding, subtracting, and multiplying matrices

Sum

If two m-by-n matrices A and B are given, we may define their sum A + B as the m-by-n matrix computed by adding corresponding elements, i.e.,

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(A + B) = A + B. For example

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:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

egin{bmatrix}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

1 & 3 & 2 \

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

1 & 0 & 0 \

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

1 & 2 & 2

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

end{bmatrix}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

+

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egin{bmatrix}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

0 & 0 & 5 \

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

7 & 5 & 0 \

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

2 & 1 & 1

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

end{bmatrix}

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