0
$\begingroup$

Consider the vectors $X_1=(1,3,2)$ and $X_2=(-2,4,3)$ in $\mathbb R^3$. Show that the set spanned by $X_1$ and $X_2$ is given by $\{(Y_1,Y_2,Y_3):Y_1-7Y_2+10Y_3=0\}$.

$\endgroup$
  • $\begingroup$ Can you please show what you have tried so far? This seems like a standard homework exercise. $\endgroup$ – air Sep 3 '15 at 13:44
  • $\begingroup$ I think the question is wrong because- $\alpha-2\beta=1$, $3\alpha+4\beta=-7$ and $2\alpha+3\beta=10$. These system of equations does not have any solution. $\endgroup$ – Rajat Sep 3 '15 at 13:58
1
$\begingroup$

The vector product of the two vectors given is

$$\vec n=X_1\times X_2=(1,-7,10).$$

All vectors in the spanned plane will be perpendicular to $\vec n$. So, the equation is $$\vec v\cdot \vec n =0.$$

Or, if $\vec v=(x,y,z)$ then the equation is

$$x-7y+10z=0.$$

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Hint: The spannig set is a plane passing through the points (1,3,2) and (-2,4,3).

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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