Multiply the Matrices [[2,-3],[1,4]][[-12,12],[13,-13]]

Problem

[[2,−3],[1,4]]*[[−12,12],[13,−13]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so the resulting product will also be a 2×2 matrix.

2. Calculate the element in the first row, first column by taking the dot product of the first row of the first matrix and the first column of the second matrix.

2*(−12)+(−3)*(13)=−24−39=−63

3. Calculate the element in the first row, second column by taking the dot product of the first row of the first matrix and the second column of the second matrix.

2*(12)+(−3)*(−13)=24+39=63

4. Calculate the element in the second row, first column by taking the dot product of the second row of the first matrix and the first column of the second matrix.

1*(−12)+4*(13)=−12+52=40

5. Calculate the element in the second row, second column by taking the dot product of the second row of the first matrix and the second column of the second matrix.

1*(12)+4*(−13)=12−52=−40

6. Assemble the resulting values into the final matrix.

Final Answer

[[2,−3],[1,4]]*[[−12,12],[13,−13]]=[[−63,63],[40,−40]]

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