Multiply the Matrices

Problem

[[1,2],[4,7]]*[[16,2],[64,7]]*[[−7,2],[4,−1]]

Solution

1. Multiply the first two matrices by calculating the dot product of rows from the first and columns from the second.

[[1,2],[4,7]]*[[16,2],[64,7]]=[[(1)*(16)+(2)*(64),(1)*(2)+(2)*(7)],[(4)*(16)+(7)*(64),(4)*(2)+(7)*(7)]]

2. Simplify the arithmetic for the resulting product matrix.

[[16+128,2+14],[64+448,8+49]]=[[144,16],[512,57]]

3. Multiply this intermediate result by the third matrix.

[[144,16],[512,57]]*[[−7,2],[4,−1]]=[[(144)*(−7)+(16)*(4),(144)*(2)+(16)*(−1)],[(512)*(−7)+(57)*(4),(512)*(2)+(57)*(−1)]]

4. Simplify the final arithmetic to find the resulting matrix elements.

[[−1008+64,288−16],[−3584+228,1024−57]]=[[−944,272],[−3356,967]]

Final Answer

[[1,2],[4,7]]*[[16,2],[64,7]]*[[−7,2],[4,−1]]=[[−944,272],[−3356,967]]

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