Multiply the Matrices [[2,4],[3,1]]*[[x,4],[y,12]]

Problem

[[2,4],[3,1]]*[[x,4],[y,12]]

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 first row, first column entry by taking the dot product of the first row of the left matrix and the first column of the right matrix.

2*(x)+4*(y)=2*x+4*y

3. Calculate the first row, second column entry by taking the dot product of the first row of the left matrix and the second column of the right matrix.

2*(4)+4*(12)=8+48=56

4. Calculate the second row, first column entry by taking the dot product of the second row of the left matrix and the first column of the right matrix.

3*(x)+1*(y)=3*x+y

5. Calculate the second row, second column entry by taking the dot product of the second row of the left matrix and the second column of the right matrix.

3*(4)+1*(12)=12+12=24

6. Combine the results into the final matrix structure.

Final Answer

[[2,4],[3,1]]*[[x,4],[y,12]]=[[2*x+4*y,56],[3*x+y,24]]

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