Multiply the Matrices [[8,6],[-3,2]][[0,1],[1,1]]

Problem

[[8,6],[−3,2]]*[[0,1],[1,1]]

Solution

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

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: 8(0) + 6(1)$.

8*(0)+6*(1)=0+6=6

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: 8(1) + 6(1)$.

8*(1)+6*(1)=8+6=14

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: −3*(0)+2*(1)

−3*(0)+2*(1)=0+2=2

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: −3*(1)+2*(1)

−3*(1)+2*(1)=−3+2=−1

6. Assemble the resulting values into the final matrix structure.

Final Answer

[[8,6],[−3,2]]*[[0,1],[1,1]]=[[6,14],[2,−1]]

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