- #1
priyathh
- 3
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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. I am not clear on the beta and gamma coordinates,
and i can't understand why the β and γ basis includes 3 vectors? I am 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?
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. I am not clear on the beta and gamma coordinates,
and i can't understand why the β and γ basis includes 3 vectors? I am 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: