Multiply the Matrices [[4,1,1],[1,4,1],[1,1,4]]*[[3],[5],[7]]

Problem

[[4,1,1],[1,4,1],[1,1,4]]*[[3],[5],[7]]

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 matrix and the column vector.

4*(3)+1*(5)+1*(7)=12+5+7=24

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

1*(3)+4*(5)+1*(7)=3+20+7=30

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

1*(3)+1*(5)+4*(7)=3+5+28=36

5. Assemble the results into the final column vector.

Final Answer

[[4,1,1],[1,4,1],[1,1,4]]*[[3],[5],[7]]=[[24],[30],[36]]

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