Multiply the Matrices [[3,1,1],[1,3,1],[1,1,3]]*[[4],[6],[8]]

Problem

[[3,1,1],[1,3,1],[1,1,3]]*[[4],[6],[8]]

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.

3*(4)+1*(6)+1*(8)=12+6+8=26

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

1*(4)+3*(6)+1*(8)=4+18+8=30

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

1*(4)+1*(6)+3*(8)=4+6+24=34

5. Assemble the results into the final column vector.

Final Answer

[[3,1,1],[1,3,1],[1,1,3]]*[[4],[6],[8]]=[[26],[30],[34]]

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