Physics Forums (http://www.physicsforums.com/index.php)
-   Calculus & Beyond Homework (http://www.physicsforums.com/forumdisplay.php?f=156)
-   -   Values for which a set of vectors form a basis of Rn (http://www.physicsforums.com/showthread.php?t=556995)

 otapia13 Dec4-11 09:06 PM

values for which a set of vectors form a basis of Rn

1. The problem statement, all variables and given/known data

For what value(s) of λ is the set of vectors {(λ^2-5, 1, 0), (2, -2, 3), (2, -3, -3)} form a basis of ℝ^3

2. Relevant equations

in order for a vector to form a basis it has to span R3 and the set has to be linearly independent.

3. The attempt at a solution
i tried doing row reduction on the matrix but i end up with identity matrix.
which means it would be a basis for any value, which is impossible.

the matrix I'm getting is [1, 0, 0 ; 0, 1, 0; λ^2 -5, 0, 4,]

anybody??

 HallsofIvy Dec5-11 04:03 AM

Re: values for which a set of vectors form a basis of Rn

What do you mean you get the identity matrix when you then write "the matrix I'm getting is [1, 0, 0 ; 0, 1, 0; λ^2 -5, 0, 4,]"? That's not row reduced. Or, rather, it is row reduced if and only if λ^2 -5= 0.

 All times are GMT -5. The time now is 09:29 PM.

Powered by vBulletin Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums