Multiply the Matrices [[4,2],[5,6]][[7,1],[2,1]]

Problem

[[4,2],[5,6]]*[[7,1],[2,1]]

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.

4*(7)+2*(2)=28+4=32

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.

4*(1)+2*(1)=4+2=6

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.

5*(7)+6*(2)=35+12=47

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.

5*(1)+6*(1)=5+6=11

6. Assemble the results into the final matrix.

Final Answer

[[4,2],[5,6]]*[[7,1],[2,1]]=[[32,6],[47,11]]

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