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June 8th, 2007, 10:43 AM   #1
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Vector Algebra Question

Hi all,

I apologise if this is in the wrong forum, not quite sure how the schooling system works over your side of the pond, but anyways, was hoping you could help me?

I have a question on my Canadian math course (I'm studying from the UK, though) the question is:

If a = 3x + 2y and b = 5x- 4y, find x and y in terms of a and b.

a, b, x and y are vectors shown in the question.

I have the solution in my answerbook, but I cannot make heads or tails of how they arrived at that answer. If someone could explain it to me I'd be very grateful!

Thanks in advance.
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June 8th, 2007, 11:18 AM   #2
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What is the solution given in your answerbook? It may be a misprint, since the problem is quite easy.
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June 8th, 2007, 01:46 PM   #3
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You have two linear equations in two unknowns. This is the simplest possible system. The fact that the letters stand for vectors rather than numbers makes no difference.
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June 8th, 2007, 06:39 PM   #4
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The exercise does not call for creating a simpler system, but, rather, for creating an equivalent system of the same level of complexity. Try adding multiples of the equations together in such a way as to cancel out either a or b.
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June 8th, 2007, 10:39 PM   #5
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Bear in mind that from an academic standpoint, there is virtually no math in my background at all. I'm quite capable of understanding the concepts behind the math, it's only that I've not come across many of these concepts before. Essentially I'm learning from scratch.

The solution given in the answerbook is:

x = (2/11)*a + (1/11)*b
y = (5/22)*a - (3/22)*b

Can someone walk me through the steps necessary to work this out please?
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June 9th, 2007, 12:17 PM   #6
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To find a in terms of x and y, you would multiply one of the equations by a real number so that the equations have the same coefficient for b, then subtract the two equations. You would then solve this new equation for a.

You can use the same process to find b in terms of x and y.
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June 10th, 2007, 02:50 PM   #7
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Re: Vector Algebra Question

Double the first equation, then add the second to it, giving 2a + b = 6x + 4y + 5x - 4y = 11x.

Hence x = (2a + b)/11. You can now find y, I hope.

The method used is to do something which makes the problem simpler, so that progress is then easier. By definition, the two sides of an equation are equal, so you can do the same thing to them both and maintain that equality.
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June 11th, 2007, 11:13 AM   #8
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Okay, got it. Thanks skipjack.
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