Multiply the Matrices [[2,3],[4,8]]*[[12,15],[4,6]]

Problem

([2,3],[4,8])*([12,15],[4,6])

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*(12)+3*(4)=24+12=36

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*(15)+3*(6)=30+18=48

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*(12)+8*(4)=48+32=80

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*(15)+8*(6)=60+48=108

6. Assemble the results into the final matrix.

Final Answer

([2,3],[4,8])*([12,15],[4,6])=([36,48],[80,108])

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