Thread: Need help, test coming soon!

Need explanations!

My test is coming up real soon!

Need help with these questions.

Sorry for the rudeness ... tests make me... nervous...

Describe all vectors v = [x,y] that are orthogonal to u = [a,b].

And I really really need help understanding "span" in linear algebra. How do you determine if a vector is the span of a matrix?

prob) determine if the vector b is in the span of the columns of the matrix A.
A =
[1 2]
[3 4]
b =
[5]
[6]

prob) show that R^2 =
span
([1] , [1])
([1] , [-1])

Hello

Since I don't know much about span, I'll take the easy one

Originally Posted by aeubz

Describe all vectors v = [x,y] that are orthogonal to u = [a,b].

Take the dot product of and



The vectors are orthogonal when

So , we see that

Now, we need to manipulate the vector :



Since, ,

Since is another constant, let's denote it by

So all the possible vectors will take on the form .

Does this make sense?

--Chris