Exercise about subvectorial space

[Malher400]

Can you guys help me with this exercise? This is from my Linear Algebra subject from Math degree. Thank you.

Translated, it says: What can be said of the geometric sequences in the vectorial subspace V_(p,q) if p^2-4q=0? In that case, find the value of each x_n term depending on n, x_1, x_2 and p.

 

[Deleted member 4993]

Can you guys help me with this exercise? This is from my Linear Algebra subject from Math degree. Thank you.

Translated, it says: What can be said of the geometric sequences in the vectorial subspace V_(p,q) if p^2-4q=0? In that case, find the value of each x_n term depending on n, x_1, x_2 and p.

Please share your work/thoughts about this assignment.

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[Dr.Peterson]

Can you guys help me with this exercise? This is from my Linear Algebra subject from Math degree. Thank you.

Translated, it says: What can be said of the geometric sequences in the vectorial subspace V_(p,q) if p^2-4q=0? In that case, find the value of each x_n term depending on n, x_1, x_2 and p.

I think we need to see the context of the question, particularly any definitions or theorems you have been given that explain what is meant by [MATH]V_{p, q}[/MATH] and [MATH]x_n[/MATH].

 

[HallsofIvy]

The problem I have with this is that "p^2- 4q= 0" isn't linear so (p, q) satisfying it does NOT form a subspace. If (p, q) satisfies p^2- 4q= 0 and (a, b) satisfies a^2- 4b= 0 then for (a+ p, b+ q), (a+ p)^2- 4(b+ q)= a^2+ 2ap+ p^2- 4b- 4a= (a^2- 4b)+ (p^2- 4q)+ 3ap= 2ap, not 0.