Introduction to Linear Algebra: Solving Real-World Problems

[xidios]

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)
Please help

 

[DrClaude]

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

 

[xidios]

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

 

[xidios]

Sorry, but my attempt is in Russian

 

[xidios]

What I sent for task 3 is already a decision

 

[WWGD]

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

 

[xidios]

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

 

[xidios]

i will add result of second task later.

 

[WWGD]

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.

 

[xidios]

Remember that a subspace or vector space in general must contain the origin.

Ok, thank you

 

[xidios]