Simplify the Matrix

Problem

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

Solution

1. Multiply the first two matrices together.

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

2. Simplify the resulting matrix from the first multiplication.

[[1,−3/2],[1,1/2]]

3. Multiply this result by the third matrix.

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

4. Calculate the final entries to obtain the simplified matrix.

[[−1−3,1+0],[−1+1,1+0]]=[[−4,1],[0,1]]

Final Answer

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

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