Simplify the Matrix

Problem

[[0,5],[1,1]]*[[1,4],[1,−2]]*[[−1/5,1],[1/5,0]]

Solution

1. Multiply the first two matrices together using the row-by-column rule.

[[0,5],[1,1]]*[[1,4],[1,−2]]=[[(0)*(1)+(5)*(1),(0)*(4)+(5)*(−2)],[(1)*(1)+(1)*(1),(1)*(4)+(1)*(−2)]]

2. Simplify the resulting product matrix.

[[5,−10],[2,2]]

3. Multiply this result by the third matrix.

[[5,−10],[2,2]]*[[−1/5,1],[1/5,0]]=[[(5)*(−1/5)+(−10)*(1/5),(5)*(1)+(−10)*(0)],[(2)*(−1/5)+(2)*(1/5),(2)*(1)+(2)*(0)]]

4. Calculate the final entries of the resulting matrix.

[[−1−2,5+0],[−2/5+2/5,2+0]]=[[−3,5],[0,2]]

Final Answer

[[0,5],[1,1]]*[[1,4],[1,−2]]*[[−1/5,1],[1/5,0]]=[[−3,5],[0,2]]

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