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Stack Exchange
05:00
rob has unfrozen this room.
Bernardo Meurer
Bernardo Meurer
Let $B=(u,v,w)$ and $B_1=(u+v,-w,u-v)$ be bases of $\mathbb R^3$ and $x_B=(2,-1,1)$. What will be the coordinates of $x$ on base $B_1$, ($x_{B_1}$)?
DanielSank
DanielSank
yo
Bernardo Meurer
Bernardo Meurer
Yo
$u, v, w$ are vectors
Not values
DanielSank
DanielSank
Oh
Jeez.
Ok.
Now I understand the question.
So where are you stuck?
Bernardo Meurer
Bernardo Meurer
A) $(1/2,-1,3/2)$ B) $(3,-1,2)$ C) $(-1,1/2,3/2)$ D) $(3,1,-1)$
I have no clue how to do this :)
DanielSank
DanielSank
05:05
Oh give me a break. Yes you do.
Bernardo Meurer
Bernardo Meurer
I swear to god I don't remember
DanielSank
DanielSank
Then figure it out by reasoning.
Bernardo Meurer
Bernardo Meurer
Sigh
Some help you are
DanielSank
DanielSank
$x_B = (2,-1,1)$. What does that mean?
Bernardo Meurer
Bernardo Meurer
it means $2u-v+w$
Ah
DanielSank
DanielSank
05:06
Yep. Now what's your goal?
Bernardo Meurer
Bernardo Meurer
They are vectors
Not values
We think dumb alike
I want $2u-v+w = \alpha(u+v) -\beta w + \gamma(u-v)$
@DanielSank ?
DanielSank
DanielSank
yes
Bernardo Meurer
Bernardo Meurer
Can I solve this with a matrix?
or should I just plug in values?
DanielSank
DanielSank
Meh. With three you can probably just guess.
Can obviously also use a matrix.
Bernardo Meurer
Bernardo Meurer
C) and D) are impossible
because of the w part
DanielSank
DanielSank
05:13
oh lol it's multiple choice.
What you need me for?
u got dis
Bernardo Meurer
Bernardo Meurer
I just was being stupid :)
DanielSank
DanielSank
Standard undergrad operating procedure.
Bernardo Meurer
Bernardo Meurer
lol

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