Multiply the Matrices

Problem

[[4316.95,−7555.5,3275],[−7555.5,13245,−5740],[3275,−5750,2500]]*[[34.2],[39.62],[46.34]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 3×3 matrix and the second is a 3×1 column vector. The resulting matrix will be a 3×1 column vector.

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

4316.95*(34.2)+(−7555.5)*(39.62)+3275*(46.34)

147639.69−299348.91+151763.5=54.28

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

−7555.5*(34.2)+13245*(39.62)+(−5740)*(46.34)

−258398.1+524766.9−266001.6=367.2

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

3275*(34.2)+(−5750)*(39.62)+2500*(46.34)

112005−227815+115850=40

Final Answer

[[4316.95,−7555.5,3275],[−7555.5,13245,−5740],[3275,−5750,2500]]*[[34.2],[39.62],[46.34]]=[[54.28],[367.2],[40]]

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