Multiply the Matrices [[1,4],[-2,3],[1,-2]]*[[w,x],[y,z]]

Problem

[[1,4],[−2,3],[1,−2]]*[[w,x],[y,z]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 3×2 and the second is 2×2 so the resulting matrix will be 3×2

2. Calculate the first row of the product by taking the dot product of the first row of the left matrix with each column of the right matrix.

1*(w)+4*(y)=w+4*y

1*(x)+4*(z)=x+4*z

3. Calculate the second row of the product by taking the dot product of the second row of the left matrix with each column of the right matrix.

−2*(w)+3*(y)=−2*w+3*y

−2*(x)+3*(z)=−2*x+3*z

4. Calculate the third row of the product by taking the dot product of the third row of the left matrix with each column of the right matrix.

1*(w)+(−2)*(y)=w−2*y

1*(x)+(−2)*(z)=x−2*z

5. Assemble the calculated entries into the final 3×2 matrix.

Final Answer

[[1,4],[−2,3],[1,−2]]*[[w,x],[y,z]]=[[w+4*y,x+4*z],[−2*w+3*y,−2*x+3*z],[w−2*y,x−2*z]]

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