Multiply the Matrices

Problem

[[6,4,2]]*[[3,2,1],[2,4/3,2/3],[3/2,1,1/2]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 1×3 and the second is 3×3 so the resulting matrix will be 1×3

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

6*(3)+4*(2)+2*(3/2)=18+8+3=29

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

6*(2)+4*(4/3)+2*(1)=12+16/3+2=14+16/3=42/3+16/3=58/3

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

6*(1)+4*(2/3)+2*(1/2)=6+8/3+1=7+8/3=21/3+8/3=29/3

5. Combine the calculated elements into the final row matrix.

Final Answer

[[6,4,2]]*[[3,2,1],[2,4/3,2/3],[3/2,1,1/2]]=[[29,58/3,29/3]]

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