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

Problem

[[1,1]]*[[1,0,1],[3,−1,1]]

Solution

1. Check dimensions to ensure the multiplication is defined. The first matrix is 1×2 and the second matrix is 2×3 Since the number of columns in the first equals the number of rows in the second, the resulting matrix will be 1×3

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

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

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

(1)*(0)+(1)*(−1)=0−1=−1

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

(1)*(1)+(1)*(1)=1+1=2

5. Assemble the results into the final 1×3 row matrix.

Final Answer

[[1,1]]*[[1,0,1],[3,−1,1]]=[[4,−1,2]]

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