buckaroobill

04-19-2007, 07:06 PM

This problem was confusing me so any help would be greatly appreciated!!

(Note that E stands for epsilon and "dot" implies the dot product symbol)

Let V be a subspace of R^n with dim(v) = n - 1. (Such a subspace is called a hyperplane in R^n.) Prove that there is a nonzero x E R^n such that

V = {v E R^n | x dot v = 0}.

(Do so by setting up a homogeneous system of equations whose coefficient matrix has a basis for V as its rows. Then notice that this (n-1) by n system has at least one nontrivial solution, say x.)

(Note that E stands for epsilon and "dot" implies the dot product symbol)

Let V be a subspace of R^n with dim(v) = n - 1. (Such a subspace is called a hyperplane in R^n.) Prove that there is a nonzero x E R^n such that

V = {v E R^n | x dot v = 0}.

(Do so by setting up a homogeneous system of equations whose coefficient matrix has a basis for V as its rows. Then notice that this (n-1) by n system has at least one nontrivial solution, say x.)