Simplify the Matrix [[m,n],[x,y]][[3,-1],[3,4]]

Problem

[[m,n],[x,y]]*[[3,−1],[3,4]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so the resulting product will also be a 2×2 matrix.

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.

m(3)+n(3)=3*m+3*n

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.

m*(−1)+n(4)=−m+4*n

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.

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

x*(−1)+y(4)=−x+4*y

6. Combine these results into the final matrix structure.

Final Answer

[[m,n],[x,y]]*[[3,−1],[3,4]]=[[3*m+3*n,−m+4*n],[3*x+3*y,−x+4*y]]

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