Multiply the Matrices [[2,3],[-1,2]][[4,1],[0,6]]

Problem

[[2,3],[−1,2]]*[[4,1],[0,6]]

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.

2*(4)+3*(0)=8+0=8

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*(1)+3*(6)=2+18=20

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*(4)+2*(0)=−4+0=−4

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*(1)+2*(6)=−1+12=11

6. Assemble the resulting values into the final 2×2 matrix.

Final Answer

[[2,3],[−1,2]]*[[4,1],[0,6]]=[[8,20],[−4,11]]

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