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

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Misplaced Homework Thread
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

Безымянный.png

3. Prove that the functions e ^ -t, e ^ -2t, e ^ -3t are linearly independent on [0,infinity)
Please help
 
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  • #2
DrClaude
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You'll have to provide an attempt at a solution.
 
  • #4
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Sorry, but my attempt is in Russian
 
  • #5
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What I sent for task 3 is already a decision
 
  • #6
WWGD
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If you're still trying to do 1, I assume it means an open ball. Does it contain the origin ?
 
  • #7
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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
 
  • #8
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i will add result of second task later.
 
  • #9
WWGD
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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.
 
  • #10
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Remember that a subspace or vector space in general must contain the origin.
Ok, thank you
 
  • #11
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IFtMOnrgv_I.jpg
 

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