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Linear algebra ordered basis problem

  • Thread starter priyathh
  • Start date
  • #1
3
0
1. The problem statement

find the β coordinates ([x]β) and γ coordinates ([x]γ) of the vector [tex]x = \begin{pmatrix}-1\\-13\\
9\\
\end{pmatrix}
\in\mathbb R[/tex]

if [tex]{β= \begin{pmatrix}-1\\4\\
-2\\
\end{pmatrix},\begin{pmatrix}3\\-1\\
-2\\
\end{pmatrix},\begin{pmatrix}2\\-5\\
1\\
\end{pmatrix}}[/tex] and [tex]{γ= \begin{pmatrix}3\\-1\\
-2\\
\end{pmatrix},\begin{pmatrix}1\\4\\
-2\\
\end{pmatrix},\begin{pmatrix}2\\-5\\
1\\
\end{pmatrix}}[/tex]


3. The Attempt at a Solution

i read my notes and as i understood it, an ordered basis is the linear combination that you use to obtain a specific vector in a vector space. im not clear on the beta and gamma coordinates,
and i cant understand why the β and γ basis includes 3 vectors? im thinking on the lines that x is obtained through a combination between the β coordinates and the given β , but that does not get me anywhere. please someone point me in the right direction! thank you

edit : ok i understand that β times the β coordinates would give the vector before the transformation, and γ
times the γ coordinates give the vector after transformation. but what exactly is x then? the vector before transformation or the vector after transformation?
 
Last edited:

Answers and Replies

  • #2
3
0
ok i have finally managed to get an answer for this question but im not sure of it at all, this is what i did

[β]x(a,b,c,d) = x where (a,b,c,d) is the beta coordinate of x

and i solved this equation and ended up getting some values for a b c and d which i wrote down as the β coordinates. is this wrong?
 
  • #3
3
0
our instructor solved this problem so anyone wanna know the solution just let me know :)
 
  • #4
4
1
our instructor solved this problem so anyone wanna know the solution just let me know :)
I would like to know.
 

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