Multiply the Matrices [[1/12,-1/6],[5/24,1/12]][[-2],[-31]]

Problem

[[1/12,−1/6],[5/24,1/12]]*[[−2],[−31]]

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 by multiplying the first row of the first matrix by the column of the second matrix.

1/12*(−2)+(−1/6)*(−31)

3. Simplify the first entry calculation.

−2/12+31/6

−1/6+31/6=30/6=5

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

5/24*(−2)+1/12*(−31)

5. Simplify the second entry calculation.

−10/24−31/12

−5/12−31/12=−36/12=−3

6. Combine the results into the final column matrix.

[[5],[−3]]

Final Answer

[[1/12,−1/6],[5/24,1/12]]*[[−2],[−31]]=[[5],[−3]]

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