Simplify the Matrix

Problem

3⋅[[1,1,1],[1,1,−1],[1,−1,1]]⋅[[1,2,3],[−1,2,4],[0,5,1]]

Solution

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

2. Calculate the element in the first row, first column: (1)*(1)+(1)*(−1)+(1)*(0)=0

3. Calculate the remaining elements of the product matrix:

(R_1):[(1)*(2)+(1)*(2)+(1)*(5)]=9,[(1)*(3)+(1)*(4)+(1)*(1)]=8

(R_2):[(1)*(1)+(1)*(−1)+(−1)*(0)]=0,[(1)*(2)+(1)*(2)+(−1)*(5)]=−1,[(1)*(3)+(1)*(4)+(−1)*(1)]=6

(R_3):[(1)*(1)+(−1)*(−1)+(1)*(0)]=2,[(1)*(2)+(−1)*(2)+(1)*(5)]=5,[(1)*(3)+(−1)*(4)+(1)*(1)]=0

4. Combine these results into the intermediate product matrix:

[[0,9,8],[0,−1,6],[2,5,0]]

5. Distribute the scalar 3 to every element inside the resulting matrix.

Final Answer

3⋅[[1,1,1],[1,1,−1],[1,−1,1]]⋅[[1,2,3],[−1,2,4],[0,5,1]]=[[0,27,24],[0,−3,18],[6,15,0]]

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