Question 151063
When you multiply matrices, you multiply rows of one with columns of the other. 
{{{(matrix(3,3,a,b,c,d,e,f,h,i,j))*(matrix(3,1,x,y,z))=(matrix(3,1,ax+by+cz,dx+ey+fz,hx+iy+jz))}}}
Let's use your numbers.
{{{(matrix(3,3,5,2,1,1,-3,-1,1,2,4))*(matrix(3,1,-3,1,2))=(matrix(3,1,5(-3)+2(1)+1(2),(1)(-3)+(-3)(1)+(-1)(2),(1)(-3)+2(1)+4(2)))}}}
{{{(matrix(3,3,5,2,1,1,-3,-1,1,2,4))*(matrix(3,1,-3,1,2))=(matrix(3,1,-11,-8,7))}}}