Multiply the Matrices

Problem

[[1,−2,1],[1,1,0],[2,−2,−5]]*[[1],[3],[1]]

Solution

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

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

1*(1)+(−2)*(3)+1*(1)=1−6+1=−4

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

1*(1)+1*(3)+0*(1)=1+3+0=4

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

2*(1)+(−2)*(3)+(−5)*(1)=2−6−5=−9

5. Assemble the resulting values into a new 3×1 matrix.

Final Answer

[[1,−2,1],[1,1,0],[2,−2,−5]]*[[1],[3],[1]]=[[−4],[4],[−9]]

Want more problems? Check here!