Add [[1,3],[-9,-6]][[6],[-7]]

Problem

[[1,3],[−9,−6]]*[[6],[−7]]

Solution

1. Identify the operation as matrix multiplication between a 2×2 matrix and a 2×1 column vector.

2. Calculate the first entry of the resulting vector by taking the dot product of the first row of the matrix and the column vector.

1*(6)+3*(−7)

6−21=−15

3. Calculate the second entry of the resulting vector by taking the dot product of the second row of the matrix and the column vector.

−9*(6)+(−6)*(−7)

−54+42=−12

4. Combine the results into a new 2×1 column vector.

Final Answer

[[1,3],[−9,−6]]*[[6],[−7]]=[[−15],[−12]]

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