Question

Finding a homogeneous linear system of two equations in 3 unknowns whose solution space has vectors in R^3 that are orthogonal a=<-3,2 -1> b=<0,-2,-2>?

Answer 1

Don't quite understand what this question is asking could someone help explain? Also suppose to find the geometric object of the solution space?

Answer 2

-3x+2y-z=0
0x-2y-2z=0

Answer 3

if you are unsure why this works..recall (I assumed you learned this) that the row space is orthogonal to the null space