Matrix x vector

Question

matrix x vector multiplication

Are these correct? When I calculated them I got -2,1,3 for the first and 1,0,-2 for the second. if I am incorrect, what have I done wrong?

Answer 1

The results you have shown in the linked image and the question text do not match. The correct values are

a) $$ \left| \matrix{ 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1} \right| \pmatrix{1 \\ 2 \\ 3} = \pmatrix{(-1)(2) \\ (1)(1) \\ (1)(3)} = \pmatrix{-2 \\ 1 \\ 3} \;\;\checkmark$$

b) $$ \left| \matrix{ 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1} \right| \pmatrix{0 \\ -1 \\ -2} = \pmatrix{(-1)(-1) \\ (1)(0) \\ (1)(-2)} = \pmatrix{1 \\ 0 \\ -2} \;\;\checkmark$$

Answer 2

I think you did a mistake on the picture on the last rows (either on matrix A) or on both of your calculation, as $1*3 \neq -3$ and $1*(-2) \neq 2$. Else, you are correct.