Multiply the Matrices

Problem

[[−1/3,−1/2],[1,1]]*[[6138,3070],[−46650,−23326]]

Solution

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

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.

−1/3*(6138)+(−1/2)*(−46650)=−2046+23325=21279

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.

−1/3*(3070)+(−1/2)*(−23326)=−3070/3+11663

−3070/3+34989/3=31919/3

4. 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*(6138)+1*(−46650)=6138−46650=−40512

5. 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*(3070)+1*(−23326)=3070−23326=−20256

Final Answer

[[−1/3,−1/2],[1,1]]*[[6138,3070],[−46650,−23326]]=[[21279,31919/3],[−40512,−20256]]

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