Multiply the Matrices [[1,0,1],[0,1,0]][[1],[2],[3]]

Problem

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

Solution

1. Identify the dimensions of the matrices. The first matrix is 2×3 and the second matrix is 3×1 Since the number of columns in the first matrix matches the number of rows in the second, the resulting matrix will be 2×1

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

1*(1)+0*(2)+1*(3)=1+0+3=4

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

0*(1)+1*(2)+0*(3)=0+2+0=2

4. Assemble the resulting elements into a 2×1 matrix.

Final Answer

[[1,0,1],[0,1,0]]*[[1],[2],[3]]=[[4],[2]]

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