Multiply the Matrices [[8,-1],[-7/2,1/2]][[1],[-5]]

Problem

[[8,−1],[−7/2,1/2]]*[[1],[−5]]

Solution

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

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

8*(1)+(−1)*(−5)

8+5=13

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

−7/2*(1)+1/2*(−5)

−7/2−5/2=−12/2=−6

4. Combine the results into a single column vector.

Final Answer

[[8,−1],[−7/2,1/2]]*[[1],[−5]]=[[13],[−6]]

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