Multiply the Matrices

Problem

[[−2,4/3,−4/3],[1,1/3,2/3],[0,1/3,−1/3]]*[[2],[1],[1]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 3×3 and the second is 3×1 so the resulting matrix will be 3×1

2. Calculate the first element by multiplying the first row of the first matrix by the column vector.

−2*(2)+4/3*(1)+(−4/3)*(1)=−4+4/3−4/3=−4

3. Calculate the second element by multiplying the second row of the first matrix by the column vector.

1*(2)+1/3*(1)+2/3*(1)=2+1/3+2/3=2+1=3

4. Calculate the third element by multiplying the third row of the first matrix by the column vector.

0*(2)+1/3*(1)+(−1/3)*(1)=0+1/3−1/3=0

Final Answer

[[−2,4/3,−4/3],[1,1/3,2/3],[0,1/3,−1/3]]*[[2],[1],[1]]=[[−4],[3],[0]]

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