Multiply the Matrices [[-9,8],[-1,-4]][[4,-2],[-1,3]]

Problem

[[−9,8],[−1,−4]]*[[4,−2],[−1,3]]

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.

(−9)*(4)+(8)*(−1)=−36−8=−44

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.

(−9)*(−2)+(8)*(3)=18+24=42

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.

(−1)*(4)+(−4)*(−1)=−4+4=0

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.

(−1)*(−2)+(−4)*(3)=2−12=−10

6. Assemble the resulting values into the final matrix structure.

Final Answer

[[−9,8],[−1,−4]]*[[4,−2],[−1,3]]=[[−44,42],[0,−10]]

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