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^25, 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?? 
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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