Find a basis perpendicular to W.

Let and

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

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- Apr 17th 2010, 02:29 PMmybrohshi5Basis perpendicular to a subspace spanned by 2 vectors
Find a basis perpendicular to W.

Let and

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 - Apr 17th 2010, 02:48 PMdwsmith
- Apr 17th 2010, 06:08 PMmybrohshi5
The question doesnt specify. It just says....... let W the subspace of spanned by v and u. Find a basis of .

I should probably know how to find both though im sure :) - Apr 17th 2010, 06:13 PMdwsmith
If you can tell me what the answer is, I can tell you what one it is looking for.

- Apr 17th 2010, 06:42 PMmybrohshi5
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

- Apr 17th 2010, 06:47 PMdwsmith
Both would be of that form.

Use the Gram-Schmidt process.

Do you know it? - Apr 17th 2010, 06:57 PMmybrohshi5
- Apr 17th 2010, 06:59 PMdwsmith
You can normalize it if you would like.

- Apr 18th 2010, 09:56 AMmybrohshi5
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

and

i plugged those in and they were wrong.

so i normalized those to get the orthononormal vectors

and

Can you see where i am going wrong? - Apr 18th 2010, 10:03 AMdwsmith
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?

- Apr 18th 2010, 10:49 AMmybrohshi5
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.... - Apr 18th 2010, 10:55 AMmybrohshi5
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 - Apr 18th 2010, 03:40 PMzzzoak
I got these

(-68, -16, 0, 1)

( -1, 0, 1, 0). - Apr 18th 2010, 05:24 PMmybrohshi5
- Apr 18th 2010, 07:33 PMdwsmith
When I followed that example, I obtained