Multiply the Matrices [[1/15,-1/5],[4/15,1/5]]*[[9],[-27]]

Problem

[[1/15,−1/5],[4/15,1/5]]*[[9],[−27]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 2×2 and the second is 2×1 resulting in a 2×1 matrix.

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

1/15*(9)+(−1/5)*(−27)

3. Simplify the first entry calculation.

9/15+27/5

3/5+27/5=30/5=6

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

4/15*(9)+1/5*(−27)

5. Simplify the second entry calculation.

36/15−27/5

12/5−27/5=−15/5=−3

Final Answer

[[1/15,−1/5],[4/15,1/5]]*[[9],[−27]]=[[6],[−3]]

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