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Problem

[[0.70,0.05,0.10],[0.20,0.70,0.15],[0.10,0.25,0.75]]*[[19462.5],[30612.5],[49925]]

Solution

1. Identify the operation as matrix multiplication between a 3×3 matrix and a 3×1 column vector.

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

0.70*(19462.5)+0.05*(30612.5)+0.10*(49925)=13623.75+1530.625+4992.5=20146.875

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

0.20*(19462.5)+0.70*(30612.5)+0.15*(49925)=3892.5+21428.75+7488.75=32810

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

0.10*(19462.5)+0.25*(30612.5)+0.75*(49925)=1946.25+7653.125+37443.75=47043.125

Final Answer

[[0.70,0.05,0.10],[0.20,0.70,0.15],[0.10,0.25,0.75]]*[[19462.5],[30612.5],[49925]]=[[20146.875],[32810],[47043.125]]

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