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

Problem

[[2,0,3],[1,1,1]]*[[2],[−1],[1]]

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 Since the number of columns in the first equals the number of rows in the second, the result will be 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 of the second matrix.

2*(2)+0*(−1)+3*(1)

4+0+3=7

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

1*(2)+1*(−1)+1*(1)

2−1+1=2

4. Combine the results into the final 2×1 matrix.

Final Answer

[[2,0,3],[1,1,1]]*[[2],[−1],[1]]=[[7],[2]]

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