Multiply the Matrices [[7,3],[4,11]]*[[1,1],[4,-1]]

Problem

[[7,3],[4,11]]*[[1,1],[4,−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.

7*(1)+3*(4)=7+12=19

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.

7*(1)+3*(−1)=7−3=4

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.

4*(1)+11*(4)=4+44=48

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.

4*(1)+11*(−1)=4−11=−7

6. Assemble the results into the final matrix.

Final Answer

[[7,3],[4,11]]*[[1,1],[4,−1]]=[[19,4],[48,−7]]

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