Multiply the Matrices

Problem

[[323/90,−59/90],[−59/30,29/30]]*[[1],[−3]]

Solution

1. Identify the dimensions of the matrices. We are multiplying a 2×2 matrix by a 2×1 column vector, which will result in a 2×1 vector.

2. Calculate the first entry of the resulting vector by taking the dot product of the first row of the matrix and the column vector.

323/90*(1)+(−59/90)*(−3)

3. Simplify the first entry calculation by performing the multiplication and addition.

323/90+177/90

500/90=50/9

4. Calculate the second entry of the resulting vector by taking the dot product of the second row of the matrix and the column vector.

−59/30*(1)+29/30*(−3)

5. Simplify the second entry calculation by performing the multiplication and addition.

−59/30−87/30

−146/30=−73/15

Final Answer

[[323/90,−59/90],[−59/30,29/30]]*[[1],[−3]]=[[50/9],[−73/15]]

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