Simplify the Matrix

Problem

[[−5/17,−1/17],[−2/17,3/17]]*[[−30,82],[−61,50]]

Solution

1. Factor out the common scalar 1/17 from the first matrix to simplify the arithmetic.

1/17*[[−5,−1],[−2,3]]*[[−30,82],[−61,50]]

2. Multiply the two integer matrices using the standard row-by-column rule.

[[(−5)*(−30)+(−1)*(−61),(−5)*(82)+(−1)*(50)],[(−2)*(−30)+(3)*(−61),(−2)*(82)+(3)*(50)]]

3. Calculate the individual entries of the resulting matrix.

[[150+61,−410−50],[60−183,−164+150]]=[[211,−460],[−123,−14]]

4. Distribute the scalar 1/17 back into each entry of the matrix.

[[211/17,−460/17],[−123/17,−14/17]]

Final Answer

[[−5/17,−1/17],[−2/17,3/17]]*[[−30,82],[−61,50]]=[[211/17,−460/17],[−123/17,−14/17]]

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