# Thread: Proof question - Orthogonal Vectors 2

1. ## Proof question - Orthogonal Vectors 2

How do I go about showing this:

Let $W= Span$ $\left\{ v_1, ....., v_p \right\}$. Show that if $x$ is orthogonal to each $v_j$, for $1 \leq j \leq p$, then $x$ is orthogonal to every vector in $W$.

2. If $v\in \textrm{Span}\{v_1,\ldots,v_p \}$ , there are scalars $\lambda_1,\ldots,\lambda_p$ such that:

$v=\lambda_1v_1+\ldots+\lambda_pv_p$

Then,

$==\ldots= 0$

3. you test for orthogonality by taking the _____? product. what's the magic number?

is this ____? product bi-linear (linear in each variable? or conjugate-linear if you are using complex numbers)?

if it is, can you break a ____? product down into sums of _____? products?

is 0+0+...+0 still zero?