Multiply the Matrices [[9,-1],[-4,1/2]][[-4],[-28]]

Problem

[[9,−1],[−4,1/2]]*[[−4],[−28]]

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 result by taking the dot product of the first row of the left matrix and the column of the right matrix.

(9)*(−4)+(−1)*(−28)

3. Simplify the first entry calculation.

−36+28=−8

4. Calculate the second entry of the result by taking the dot product of the second row of the left matrix and the column of the right matrix.

(−4)*(−4)+(1/2)*(−28)

5. Simplify the second entry calculation.

16−14=2

6. Combine the results into the final column matrix.

Final Answer

[[9,−1],[−4,1/2]]*[[−4],[−28]]=[[−8],[2]]

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