Multiply the Matrices [[5,6],[7,9]]*[[8,5],[3,1]]

Problem

[[5,6],[7,9]]*[[8,5],[3,1]]

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.

5*(8)+6*(3)=40+18=58

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.

5*(5)+6*(1)=25+6=31

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.

7*(8)+9*(3)=56+27=83

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.

7*(5)+9*(1)=35+9=44

6. Assemble the results into the final matrix.

Final Answer

[[5,6],[7,9]]*[[8,5],[3,1]]=[[58,31],[83,44]]

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