Recent content by sharpie

Thanks everyone. Grr, I even said in the original post: "I also noticed that if we assume that w is perpendicular to x then: w o x = det(a, b) = 0, so x must be parallel to a, which means that w is perpendicular to a. I tried to generalize this, but couldn't come up with anything. " But I didn't...

I am pretty unfamiliar with determinants, so I must be missing something. det( a, x ) = 0 whenever x is a constant multiple of a (in other words parallel?), or either a or x is zero, right? So then it can be shown that whenever x is parallel to a, w is perpendicular to a. But what about when x...

If I am understanding both of you correctly, you are saying that det(a,a) must equal 0, so a o w = 0 meaning a and w are perpendicular. Doesn't that only prove that a and w are perpendicular when x = a though? Thanks for your help.

Homework Statement In R^2, vectors x = (x1, x2) and a = (a1, a2). For fixed a, det(a, x) is a scalar-valued linear function of the vector x. Thus it can be written as the dot product of x with some fixed vector w. Explain why w is perpendicular to a. Do not use an expression of w in terms of...