Multiply the Matrices A[[5,6],[4,5]]B[[-2],[9]]

Problem

[[5,6],[4,5]]*[[−2],[9]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×2 matrix and the second is a 2×1 matrix. The resulting matrix will be a 2×1 matrix.

2. Calculate the first element of the result by taking the dot product of the first row of matrix A and the column of matrix B

5*(−2)+6*(9)

−10+54=44

3. Calculate the second element of the result by taking the dot product of the second row of matrix A and the column of matrix B

4*(−2)+5*(9)

−8+45=37

4. Combine the results into the final column matrix.

[[44],[37]]

Final Answer

[[5,6],[4,5]]*[[−2],[9]]=[[44],[37]]

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