# Thread: Basis perpendicular to a subspace spanned by 2 vectors

1. ## Basis perpendicular to a subspace spanned by 2 vectors

Find a basis perpendicular to W.

Let $V = \begin{bmatrix}1\\-4\\1\\4\end{bmatrix}$ and $U = \begin{bmatrix}3\\-13\\3\\-4\end{bmatrix}$

and let W be the subspace spanned by V and U.

I am pretty confused on this topic right now I just dont seem to know what i need to do to solve problems like these.

Any help would be great

Thank you

2. Originally Posted by mybrohshi5
Find a basis perpendicular to W.

Let $V = \begin{bmatrix}1\\-4\\1\\4\end{bmatrix}$ and $U = \begin{bmatrix}3\\-13\\3\\-4\end{bmatrix}$

and let W be the subspace spanned by V and U.

I am pretty confused on this topic right now I just dont seem to know what i need to do to solve problems like these.

Any help would be great

Thank you
Do you want an orthogonal basis or orthonormal basis?

3. The question doesnt specify. It just says....... let W the subspace of ${\mathbb R}^4$ spanned by v and u. Find a basis of $W^{\perp}$.

I should probably know how to find both though im sure

4. If you can tell me what the answer is, I can tell you what one it is looking for.

5. Im not sure what the answer is. Its for online homework.

There are two blank 4x1 matrixes where i can put my answer in. so it looks like this

$\begin{bmatrix}.\\.\\.\\.\end{bmatrix}, \begin{bmatrix}.\\.\\.\\.\end{bmatrix}$

6. Both would be of that form.

Use the Gram-Schmidt process.

Do you know it?

7. Originally Posted by dwsmith
Both would be of that form.

Use the Gram-Schmidt process.

Do you know it?
Yes i do. Is that all i have to do? Seems easy enough.

and will the Gram schmidt process give me an orthogonal basis correct? then from there i could find a orthonormal basis if i needed right?

8. You can normalize it if you would like.

9. Using the gram schmidt process is not getting me the right answer

I even normalized the orthogonal basis i got and those are wrong as well.

Using the process i got

$\begin{bmatrix}1\\-4\\1\\4\end{bmatrix}$ and $\begin{bmatrix}\frac{30}{17}\\-\frac{137}{17}\\\frac{30}{17}\\-\frac{152}{17}\end{bmatrix}$

i plugged those in and they were wrong.

so i normalized those to get the orthononormal vectors

$\frac{1}{\sqrt(34)}*\begin{bmatrix}1\\-4\\1\\4\end{bmatrix}$ and $\frac{1}{\sqrt(2569/17)}*\begin{bmatrix}\frac{30}{17}\\-\frac{137}{17}\\\frac{30}{17}\\-\frac{152}{17}\end{bmatrix}$

Can you see where i am going wrong?

10. I just checked my dot product and it wasn't zero but your dot product is. What section in your book does this question relate too?

11. This is for online homework and i dont have the book cause i am fairly good at math and the professor said we didnt need it unless we needed an extra source of help (mine is this forum haha).

If i look at the professors power points i would think it relates to the section called Orthogonal Vectors in R^n, but i am not positive....

12. I found this on yahoo answers and it looks similar to my question but i am a little unsure what is done to get the answer. maybe you will know what is going on

Find a basis of the subspace of R4 that consists of all vectors perpendicular to both:? - Yahoo! Answers

13. I got these
(-68, -16, 0, 1)
( -1, 0, 1, 0).

14. Originally Posted by zzzoak
I got these
(-68, -16, 0, 1)
( -1, 0, 1, 0).
What did you do to find those?

15. When I followed that example, I obtained $x_3\begin{bmatrix}
-1\\
0\\
1\\
0
\end{bmatrix}+x_4\begin{bmatrix}
-68\\
-16\\
0\\
1
\end{bmatrix}$

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