Multiply the Matrices

Problem

[[−1/8,3/8],[1/16,5/16]]*[[3/7,−1/7],[1/7,2/7]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so their product will also be a 2×2 matrix.

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

(−1/8⋅3/7)+(3/8⋅1/7)=−3/56+3/56=0

3. Calculate the element in the first row, second column by multiplying the first row of the first matrix by the second column of the second matrix.

(−1/8⋅−1/7)+(3/8⋅2/7)=1/56+6/56=7/56

4. Simplify the fraction for the first row, second column.

7/56=1/8

5. Calculate the element in the second row, first column by multiplying the second row of the first matrix by the first column of the second matrix.

(1/16⋅3/7)+(5/16⋅1/7)=3/112+5/112=8/112

6. Simplify the fraction for the second row, first column.

8/112=1/14

7. Calculate the element in the second row, second column by multiplying the second row of the first matrix by the second column of the second matrix.

(1/16⋅−1/7)+(5/16⋅2/7)=−1/112+10/112=9/112

Final Answer

[[−1/8,3/8],[1/16,5/16]]*[[3/7,−1/7],[1/7,2/7]]=[[0,1/8],[1/14,9/112]]

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