# Linear algebra questions (linear subspace, linearly independent functions, etc.)

Summary:: Linear algebra

1.Let a a fixed vector of the Euclidean space E, a is a fixed real number. Is there a set of all vectors from E for which (x, a) = d the linear subspace E /
2.
Let nxn be a matrix A that is not degenerate. Prove that the characteristic polynomials f (λ) of the matrix A and h (λ) of the matrix A ^ -1 are related by 3. Prove that the functions e ^ -t, e ^ -2t, e ^ -3t are linearly independent on [0,infinity)

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DrClaude
Mentor
You'll have to provide an attempt at a solution.

You'll have to provide an attempt at a solution. Sorry, but my attempt is in Russian

WWGD
Gold Member
2019 Award
If you're still trying to do 1, I assume it means an open ball. Does it contain the origin ?

If you're still trying to do 1, I assume it means an open ball. Does it contain the origin ?
I did 2, but I'm not sure what is right. The first I did not. I did not understand your question

WWGD
Gold Member
2019 Award
I did 2, but I'm not sure what is right. The first I did not. I did not understand your question
Remember that a subspace or vector space in general must contain the origin.

Remember that a subspace or vector space in general must contain the origin.
Ok, thank you 