Multiply the Matrices

Problem

[[11150.5716,−851.7326,16.1764],[−851.7326,65.1274,−1.2382],[16.1764,−1.2382,0.0236]]*[[105.1],[2742.56],[71951.926]]

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

11150.5716*(105.1)+(−851.7326)*(2742.56)+16.1764*(71951.926)

1171925.07516−2335959.85856+1163923.13574=−111.64766

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

−851.7326*(105.1)+65.1274*(2742.56)+(−1.2382)*(71951.926)

−89517.09626+178615.80414−89090.87477=7.83311

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

16.1764*(105.1)+(−1.2382)*(2742.56)+0.0236*(71951.926)

1700.13964−3395.83779+1698.06545=2.3673

Final Answer

[[11150.5716,−851.7326,16.1764],[−851.7326,65.1274,−1.2382],[16.1764,−1.2382,0.0236]]*[[105.1],[2742.56],[71951.926]]=[[−111.64766],[7.83311],[2.3673]]

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