Multiply the Matrices [[3,-2],[-5,29]][[4/4,1/7],[-3/7,1/7]]

Problem

[[3,−2],[−5,29]]*[[4/4,1/7],[−3/7,1/7]]

Solution

1. Simplify the first element of the second matrix, noting that 4/4=1

2. Calculate the first row, first column entry by multiplying the first row of the left matrix by the first column of the right matrix: 3*(1)+(−2)*(−3/7)

3+6/7=21/7+6/7=27/7

3. Calculate the first row, second column entry by multiplying the first row of the left matrix by the second column of the right matrix: 3*(1/7)+(−2)*(1/7)

3/7−2/7=1/7

4. Calculate the second row, first column entry by multiplying the second row of the left matrix by the first column of the right matrix: −5*(1)+29*(−3/7)

−5−87/7=−35/7−87/7=−122/7

5. Calculate the second row, second column entry by multiplying the second row of the left matrix by the second column of the right matrix: −5*(1/7)+29*(1/7)

−5/7+29/7=24/7

6. Combine the results into the resulting matrix.

Final Answer

[[3,−2],[−5,29]]*[[4/4,1/7],[−3/7,1/7]]=[[27/7,1/7],[−122/7,24/7]]

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