Multiply the Matrices

Problem

[[1,0,−1],[−4/3,2/3,1],[−1/3,−1/3,1]]*[[2770],[1330],[1925]]

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 row entry by taking the dot product of the first row and the column vector.

1*(2770)+0*(1330)+(−1)*(1925)=2770−1925=845

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

−4/3*(2770)+2/3*(1330)+1*(1925)=(−11080+2660)/3+1925

(−8420)/3+5775/3=−2645/3

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

−1/3*(2770)+−1/3*(1330)+1*(1925)=(−2770−1330)/3+1925

(−4100)/3+5775/3=1675/3

Final Answer

[[1,0,−1],[−4/3,2/3,1],[−1/3,−1/3,1]]*[[2770],[1330],[1925]]=[[845],[−2645/3],[1675/3]]

Want more problems? Check here!