Linear algebra help!

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hayood

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Feb 16, 2010
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Suppose an xy-coordinate system is translated to obtain an x' y' -coordinate system whose origin O' has xy-coordinates ( 2, -3).

a) If v= (3,7) is a vector in the xy-coordinate system, what are the components of v in the x' y'-coordinate system?
my answer:
x' = x -2 and y' = y+3
x' = 3 -2 y' = 7+3
x' = 1 y' = 10
so, v=(1,10)
i need to know if what i am doing is right or is there another way of doing it.

b) If v = (v1, v2) is a vector in the xy-coordinate system, what are the components of v in the x' y'-coordinate system?
for this one i wasn't sure i know how to solve it..

can someone help please:)
 
Part a) is right, and you already have part b)!:
For a vector v=(u,v), the vector v' in the new system is v'=(u-2, v-3) :D
garf
 
hayood said:
Suppose an xy-coordinate system is translated to obtain an x'y'-coordinate system whose origin O' has xy-coordinates ( 2, -3).

a) If v= (3,7) is a vector in the xy-coordinate system, what are the components of v in the x' y'-coordinate system?
Click to expand...

I'm not understanding something, in this exercise.

If we shift the xy-coordinate system horizontally and vertically, why would that change the components of any vector? It seems to me that the vector would remain unchanged; only its position, relative to the new coordinate system, would change.

In other words, we can slide the vector <3, 7> around the coordinate system as much as we like. Its components will always be <3, 7>.

If the exercise were to instead ask for the x'y'-coordinates at the head of vector v when its tail is positioned at (-2,3) in the x'y'-coordinate system, then I would report that as (1, 10).

Or, if they were to ask for the xy-coordinates at the head when the tail is positioned at (2,-3) in the xy-coordinate system, then I would report that as (5,4).

I must be missing something here. :?

What do you think?
 
ya that's what i did ..i am still not sure if that is the way it is solved.
 
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