Multiply the Matrices

Problem

[[1/3,1/3,1/3],[−1/2,0,1/2]]*[[1],[1],[0]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 2×3 and the second is 3×1 resulting in a 2×1 matrix.

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

1/3*(1)+1/3*(1)+1/3*(0)

3. Simplify the first element.

1/3+1/3+0=2/3

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

−1/2*(1)+0*(1)+1/2*(0)

5. Simplify the second element.

−1/2+0+0=−1/2

Final Answer

[[1/3,1/3,1/3],[−1/2,0,1/2]]*[[1],[1],[0]]=[[2/3],[−1/2]]

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