Linear Algebra Change of Bases problem

[kaelbu]

This problem was provided as an example in my book, but I can't figure out what is going on here:
given bases B= {(1,1), (1,-1)} and B' = { ( 2,4), (3,1)} . Let T be a linear operator defined as T (a, b) = ( 3a- b , a+3b)
[T ][sub:379vli7a]B[/sub:379vli7a] = \(\displaystyle \left( \begin{array}{cc} 3 & 1 \\ -1 & 3 \\\end{array} \right)\)

According to my calculations
T = \(\displaystyle \left(\begin{array}{cc} 3 & -1 \\ 1 & 3 \\ \end{array} \right)\)
therefore [T][sub:379vli7a]B[/sub:379vli7a] = \(\displaystyle \left(\begin{array}{cc} 2 & 1 \\ 1 & -2 \\\end{array} \right)\)
Where am I going wrong? My book insists that it is OBVIOUS and that I should be able to verify this matrix, but I can't figure it out.
Thanks for the help,

 

[Denis]

Are we supposed to be able to read that?

 

[kaelbu]

No, I thought I'd post some random gibberish just to annoy you.
Seriously?
I can read it perfectly well. I actually put some effort into formatting it, there are some superfluous <\br>s in my matrices, but they don't really hinder the reading experience at all.
The only explanation for why you can't read it that I can think of is that your computer does not support tex, which isn't my fault.

 

[soroban]

Hello, kaelbu!

When typing an array, do not use RETURN between rows.
In fact, always type a line of LaTeX in one continuous line.

This problem was provided as an example in my book, but I can't figure out what is going on here:

\(\displaystyle \text{Given bases: }\; B\:=\: \{(1,1),\1,\text{-}1)\}\,\text{ and }\,B' \:=\: ( 2,4),\3,1)\}\)

\(\displaystyle \text}Let }T\text{ be a linear operator defined as: }\:T(a, b) \:=\: ( 3a- b,\: a+3b)\)

\(\displaystyle [T ]_B \;=\;\left(\begin{array}{cc} 3 & 1 \\ -1 & 3 \\ \end{array} \right)\)


According to my calculations :

\(\displaystyle T \;=\;\left(\begin{array}{cc} 3 & \text{-}1 \\ 1 & 3 \\ \end{array} \right)\)

\(\displaystyle \text{Therefore: }\;[T]_B \;=\;\left(\begin{array}{cc} 2 & 1 \\ 1 & \text{-}2 \\ \end{array} \right)\)

Where am I going wrong? My book insists that it is OBVIOUS
and that I should be able to verify this matrix, but I can't figure it out.

"I can read it perfectly well" . . . That's because you know what it's supposed to say.


Try this one . . .

\(\displaystyle \text{Given: }\;
A
\;=\;
\left[
\begin{array}{cc}
3
&
2
\\
0
&
1
\\
\end{array}
\right]\)

. .\(\displaystyle \text{and: }\;
B
\;=\;
\left[
\begin{array}{cc}
2
&
0
\\
3
&
1
\\
\end{array}
\right]\)

\(\displaystyle \text{Find: }\;AB.\)


Annoying, isn't it?

 

[Denis]

No, I thought I'd post some random gibberish just to annoy you.

Ahhhh geeesh...what did I ever do to you to deserve your Royal Wrath?

 

[Deleted member 4993]

Dennnis - go sit in the corner and count to 42 backwards from 95.

 

[Denis]

ninety-five, ninety-four, ........fifty-seven, fifty-six, ...I'm getting there... :x

 

[kaelbu]

If you think that's royal wrath, you should see what happens when you get between me and my peanut butter.
Sorry, I yelled at you / replied snarkily. I thought that it kind of matched the tone of your statement. That's trouble with the internet, no inflection.
@soroban Thank for the help with the LaTex, I will edit my post. I do realize that the way I typed it was annoying, which is why I apologized.