Multiply the Matrices

Problem

[[−2/3,−1/3],[1,1]]*[[−1,0],[0,3125]]*[[−3,−1],[3,2]]

Solution

1. Multiply the first two matrices.

[[−2/3,−1/3],[1,1]]*[[−1,0],[0,3125]]=[[(−2/3)*(−1)+(−1/3)*(0),(−2/3)*(0)+(−1/3)*(3125)],[(1)*(−1)+(1)*(0),(1)*(0)+(1)*(3125)]]

2. Simplify the resulting matrix.

[[2/3,−3125/3],[−1,3125]]

3. Multiply this result by the third matrix.

[[2/3,−3125/3],[−1,3125]]*[[−3,−1],[3,2]]=[[(2/3)*(−3)+(−3125/3)*(3),(2/3)*(−1)+(−3125/3)*(2)],[(−1)*(−3)+(3125)*(3),(−1)*(−1)+(3125)*(2)]]

4. Calculate the individual entries.

Row 1, Col 1: −2−3125=−3127

Row 1, Col 2: −2/3−6250/3=−6252/3=−2084

Row 2, Col 1: *3+9375=9378

Row 2, Col 2: *1+6250=6251

Final Answer

[[−2/3,−1/3],[1,1]]*[[−1,0],[0,3125]]*[[−3,−1],[3,2]]=[[−3127,−2084],[9378,6251]]

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