Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having a problem with this question, I just can't seem to get it.

Consider the plane $\mathbb{R}^3$ defined by the equation $x+2y-z=0$ Find any two vectors $\mathbf{v},\mathbf{w}$ such that their span may be identified with this plane.

share|improve this question

2 Answers 2

up vote 3 down vote accepted

Let

$M=\{(x,y,z)^T\in \mathbb{R^3}:x+2y-z=0\}$

$x+2y-z=0$$\hspace{0.2cm}$$\implies$$\hspace{0.2cm}$ $z=x+2y$

So

$(x,y,z)^T=(x,y,x+2y)^T=x(1,0,1)^T+y(0,1,2)^T$

Hence

$M=\{(x,y,z)^T\in \mathbb{R^3}:x+2y-z=0\}=<(1,0,1)^T,(0,1,2)^T>$

share|improve this answer

Just take two vectors that satisfy the equation of the plane for example $$v=(-1,1,1)^T\quad;\quad w=(0,1,2)^T$$ and verify that they are linearly independent i.e. there's not $k\in\Bbb R$ such that $$v=kw$$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.