I'm a bit confused, conceptually. This is the problem Let v1=( 1, -1, 2) v2=( 2, 1, 3) v3=( 1, -4, 3) Find a nonzero vector u that is orthogonal to all three vectors v1, v2, and v3. I know how to find the projection matrix, P, which I can solve with v1, v2, and v3. The equation for that is simply p=A(AT A)^-1AT (Where AT is A transposed) However, I'm not sure exactly what P is... I know it's the projection matrix, but if I solved this, would this give me a matrix that is orthogonal to A? (Assuming A is spanned by v1, v2, and v3). If so, would I just be able to take one of the column vectors from this matrix and assume that it is orthogonal to v1 v2 and v3?? If I'm going in the wrong direction, can someone tell me how to find a vector that is orthogonal to A? Thanks!