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-   -   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.


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