Simplify the Matrix

Problem

[[0.70,0.05,0.10],[0.20,0.70,0.15],[0.10,0.25,0.75]]*[[20565.9],[34751.4],[44652.6]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 3×3 and the second is 3×1 resulting in a 3×1 matrix.

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

0.70*(20565.9)+0.05*(34751.4)+0.10*(44652.6)

14396.13+1737.57+4465.26=20598.96

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

0.20*(20565.9)+0.70*(34751.4)+0.15*(44652.6)

4113.18+24325.98+6697.89=35137.05

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

0.10*(20565.9)+0.25*(34751.4)+0.75*(44652.6)

2056.59+8687.85+33489.45=44233.89

Final Answer

[[0.70,0.05,0.10],[0.20,0.70,0.15],[0.10,0.25,0.75]]*[[20565.9],[34751.4],[44652.6]]=[[20598.96],[35137.05],[44233.89]]

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