Simplify the Matrix

Problem

[[1,0,0],[0,1,1],[0,10,1]]*[[−1,1,1],[−1,1,−1],[0,−1,0]]

Solution

1. Identify the dimensions of the matrices. Both are 3×3 matrices, so their product will also be a 3×3 matrix.

2. Calculate the first row of the resulting matrix by taking the dot product of the first row of the left matrix with each column of the right matrix.

1*(−1)+0*(−1)+0*(0)=−1

1*(1)+0*(1)+0*(−1)=1

1*(1)+0*(−1)+0*(0)=1

3. Calculate the second row of the resulting matrix by taking the dot product of the second row of the left matrix with each column of the right matrix.

0*(−1)+1*(−1)+1*(0)=−1

0*(1)+1*(1)+1*(−1)=0

0*(1)+1*(−1)+1*(0)=−1

4. Calculate the third row of the resulting matrix by taking the dot product of the third row of the left matrix with each column of the right matrix.

0*(−1)+10*(−1)+1*(0)=−10

0*(1)+10*(1)+1*(−1)=9

0*(1)+10*(−1)+1*(0)=−10

5. Combine the calculated elements into the final matrix structure.

Final Answer

[[1,0,0],[0,1,1],[0,10,1]]*[[−1,1,1],[−1,1,−1],[0,−1,0]]=[[−1,1,1],[−1,0,−1],[−10,9,−10]]

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