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Problem

[[1,−8,2,2,1],[0,2,4,0,−2],[3,−22,2,6,6],[7,−54,10,14,10],[−3,26,−2,−6,−5]]*[[w],[e],[r],[t],[y]]

Solution

1. Identify the operation as matrix-vector multiplication, where each element of the resulting vector is the dot product of a row from the matrix and the column vector.

2. Calculate the first component by multiplying the first row by the vector elements.

1*(w)+(−8)*(e)+2*(r)+2*(t)+1*(y)=w−8*e+2*r+2*t+y

3. Calculate the second component by multiplying the second row by the vector elements.

0*(w)+2*(e)+4*(r)+0*(t)+(−2)*(y)=2*e+4*r−2*y

4. Calculate the third component by multiplying the third row by the vector elements.

3*(w)+(−22)*(e)+2*(r)+6*(t)+6*(y)=3*w−22*e+2*r+6*t+6*y

5. Calculate the fourth component by multiplying the fourth row by the vector elements.

7*(w)+(−54)*(e)+10*(r)+14*(t)+10*(y)=7*w−54*e+10*r+14*t+10*y

6. Calculate the fifth component by multiplying the fifth row by the vector elements.

−3*(w)+26*(e)+(−2)*(r)+(−6)*(t)+(−5)*(y)=−3*w+26*e−2*r−6*t−5*y

Final Answer

[[1,−8,2,2,1],[0,2,4,0,−2],[3,−22,2,6,6],[7,−54,10,14,10],[−3,26,−2,−6,−5]]*[[w],[e],[r],[t],[y]]=[[w−8*e+2*r+2*t+y],[2*e+4*r−2*y],[3*w−22*e+2*r+6*t+6*y],[7*w−54*e+10*r+14*t+10*y],[−3*w+26*e−2*r−6*t−5*y]]

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