Multiply the Matrices [[8/7,-1/7],[-1/7,1/7]][[1,1],[1,8]]

Problem

[[8/7,−1/7],[−1/7,1/7]]*[[1,1],[1,8]]

Solution

1. Identify the rule for matrix multiplication, where the element in row i and column j is the dot product of the ith row of the first matrix and the jth column of the second matrix.

2. Calculate the element for the first row, first column:

8/7*(1)+(−1/7)*(1)=8/7−1/7=7/7=1

3. Calculate the element for the first row, second column:

8/7*(1)+(−1/7)*(8)=8/7−8/7=0

4. Calculate the element for the second row, first column:

−1/7*(1)+1/7*(1)=−1/7+1/7=0

5. Calculate the element for the second row, second column:

−1/7*(1)+1/7*(8)=−1/7+8/7=7/7=1

6. Combine the results into the resulting matrix.

Final Answer

[[8/7,−1/7],[−1/7,1/7]]*[[1,1],[1,8]]=[[1,0],[0,1]]

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