Multiply the Matrices

Problem

[[0,1,−1],[2,−2,−1],[−1,1,1]]*[[118],[81],[62]]

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

0*(118)+1*(81)+(−1)*(62)=0+81−62=19

3. Calculate the second entry by taking the dot product of the second row of the left matrix and the column vector.

2*(118)+(−2)*(81)+(−1)*(62)=236−162−62=12

4. Calculate the third entry by taking the dot product of the third row of the left matrix and the column vector.

−1*(118)+1*(81)+1*(62)=−118+81+62=25

5. Combine the results into the final column vector.

Final Answer

[[0,1,−1],[2,−2,−1],[−1,1,1]]*[[118],[81],[62]]=[[19],[12],[25]]

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