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

[otapia13]

Homework Statement

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

Homework Equations

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

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]

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.