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

Problem

[[2,−1,2],[0,1,0]]*[[1],[0],[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 resulting matrix will be 2×1

2. Calculate the first entry of the resulting matrix by taking the dot product of the first row of the left matrix and the column of the right matrix.

2*(1)+(−1)*(0)+2*(1)

2+0+2=4

3. Calculate the second entry of the resulting matrix by taking the dot product of the second row of the left matrix and the column of the right matrix.

0*(1)+1*(0)+0*(1)

0+0+0=0

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

Final Answer

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

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