Multiply the Matrices

Problem

[[−17/3,−4,8,−4],[−61/3,−11,25,−14],[−4,−2,5,−3],[5/3,1,−2,1]]*[[1],[2],[0],[−5]]

Solution

1. Identify the dimensions of the matrices. We are multiplying a 4×4 matrix by a 4×1 column vector, which will result in a 4×1 column vector.

2. Calculate the first element by taking the dot product of the first row and the column vector.

−17/3*(1)+(−4)*(2)+8*(0)+(−4)*(−5)=−17/3−8+0+20

−17/3+12=−17/3+36/3=19/3

3. Calculate the second element by taking the dot product of the second row and the column vector.

−61/3*(1)+(−11)*(2)+25*(0)+(−14)*(−5)=−61/3−22+0+70

−61/3+48=−61/3+144/3=83/3

4. Calculate the third element by taking the dot product of the third row and the column vector.

−4*(1)+(−2)*(2)+5*(0)+(−3)*(−5)=−4−4+0+15

−8+15=7

5. Calculate the fourth element by taking the dot product of the fourth row and the column vector.

5/3*(1)+1*(2)+(−2)*(0)+1*(−5)=5/3+2+0−5

5/3−3=5/3−9/3=−4/3

Final Answer

[[−17/3,−4,8,−4],[−61/3,−11,25,−14],[−4,−2,5,−3],[5/3,1,−2,1]]*[[1],[2],[0],[−5]]=[[19/3],[83/3],[7],[−4/3]]

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