Multiply the Matrices [[10,-1],[-9/2,1/2]][[2],[16]]

Problem

[[10,−1],[−9/2,1/2]]*[[2],[16]]

Solution

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

2. Calculate the first entry of the product by multiplying the first row of the first matrix by the column of the second matrix.

10*(2)+(−1)*(16)

20−16=4

3. Calculate the second entry of the product by multiplying the second row of the first matrix by the column of the second matrix.

−9/2*(2)+1/2*(16)

−9+8=−1

4. Combine the results into the final column matrix.

[[4],[−1]]

Final Answer

[[10,−1],[−9/2,1/2]]*[[2],[16]]=[[4],[−1]]

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