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

Problem

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

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×3 row vector and the second is a 3×3 square matrix. The resulting matrix will be a 1×3 row vector.

2. Calculate the first element of the result by multiplying the row by the first column of the second matrix.

(1)*(1)+(1)*(−1)+(1)*(0)=1−1+0=0

3. Calculate the second element of the result by multiplying the row by the second column of the second matrix.

(1)*(−1)+(1)*(2)+(1)*(1)=−1+2+1=2

4. Calculate the third element of the result by multiplying the row by the third column of the second matrix.

(1)*(1)+(1)*(−1)+(1)*(−1)=1−1−1=−1

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

Final Answer

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

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