Multiply the Matrices

Problem

[[0,−2],[4,3]]*[[3,2,−2],[6,−6,7]]+[[−4,1,4],[−6,4,−6]]

Solution

1. Multiply the first two matrices by calculating the dot product of each row from the first matrix with each column of the second matrix.

[[0*(3)+(−2)*(6),0*(2)+(−2)*(−6),0*(−2)+(−2)*(7)],[4*(3)+3*(6),4*(2)+3*(−6),4*(−2)+3*(7)]]

2. Simplify the arithmetic within the resulting product matrix.

[[−12,12,−14],[30,−10,13]]

3. Add the resulting matrix to the third matrix by summing corresponding elements.

[[−12+(−4),12+1,−14+4],[30+(−6),−10+4,13+(−6)]]

4. Simplify the final addition to obtain the result.

[[−16,13,−10],[24,−6,7]]

Final Answer

[[0,−2],[4,3]]*[[3,2,−2],[6,−6,7]]+[[−4,1,4],[−6,4,−6]]=[[−16,13,−10],[24,−6,7]]

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