Multiply the Matrices

Problem

[[2,−1],[−5,3]]*[[1,−1],[1,2]]*[[3,1],[5,2]]

Solution

1. Multiply the first two matrices.

[[2,−1],[−5,3]]*[[1,−1],[1,2]]=[[(2)*(1)+(−1)*(1),(2)*(−1)+(−1)*(2)],[(−5)*(1)+(3)*(1),(−5)*(−1)+(3)*(2)]]

2. Simplify the resulting matrix.

[[2−1,−2−2],[−5+3,5+6]]=[[1,−4],[−2,11]]

3. Multiply this result by the third matrix.

[[1,−4],[−2,11]]*[[3,1],[5,2]]=[[(1)*(3)+(−4)*(5),(1)*(1)+(−4)*(2)],[(−2)*(3)+(11)*(5),(−2)*(1)+(11)*(2)]]

4. Simplify the final matrix elements.

[[3−20,1−8],[−6+55,−2+22]]=[[−17,−7],[49,20]]

Final Answer

[[2,−1],[−5,3]]*[[1,−1],[1,2]]*[[3,1],[5,2]]=[[−17,−7],[49,20]]

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