Multiply the Matrices [[3,5],[4,1]][[3,6],[9,1]]

Problem

[[3,5],[4,1]]*[[3,6],[9,1]]

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.

3*(3)+5*(9)=9+45=54

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.

3*(6)+5*(1)=18+5=23

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*(3)+1*(9)=12+9=21

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*(6)+1*(1)=24+1=25

6. Assemble the resulting matrix using the calculated values.

Final Answer

[[3,5],[4,1]]*[[3,6],[9,1]]=[[54,23],[21,25]]

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