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Problem

[[0.30,0.20,0.30],[0.40,0.30,0.30],[0.30,0.30,0.20]]*[[81],[8],[9]]

Solution

1. Identify the matrix multiplication dimensions. We are multiplying a 3×3 matrix by a 3×1 column vector, which will result in a 3×1 column vector.

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

0.30*(81)+0.20*(8)+0.30*(9)

24.3+1.6+2.7=28.6

3. Calculate the second element of the resulting vector by taking the dot product of the second row and the column vector.

0.40*(81)+0.30*(8)+0.30*(9)

32.4+2.4+2.7=37.5

4. Calculate the third element of the resulting vector by taking the dot product of the third row and the column vector.

0.30*(81)+0.30*(8)+0.20*(9)

24.3+2.4+1.8=28.5

Final Answer

[[0.30,0.20,0.30],[0.40,0.30,0.30],[0.30,0.30,0.20]]*[[81],[8],[9]]=[[28.6],[37.5],[28.5]]

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