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October 31st, 2009, 02:55 PM
| | Junior Member | | Join Date: Aug 2009
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| |  Matrix Problem
The question is, Solve the equation!  I think I have solved the first part...
x = 8
y = -1
z = 3 But then they say that the answer has to be written as; 
Where a,b,c,d,e,f,g,h have to be itegers. I have absolutely no idea how to solve this problem. Please help! What is... a=? b=?
c=?
d=?
e=?
f=?
g=?
h=?
Thanks! |
October 31st, 2009, 03:57 PM
|  | Flow Master | | Join Date: Dec 2007 Location: Zeitgeist
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Quote:
Originally Posted by sf1903  The question is, Solve the equation! Attachment 13603 I think I have solved the first part...
x = 8
y = -1
z = 3 But then they say that the answer has to be written as; Attachment 13604
Where a,b,c,d,e,f,g,h have to be itegers. I have absolutely no idea how to solve this problem. Please help! What is... a=? b=?
c=?
d=?
e=?
f=?
g=?
h=?
Thanks! | You have not correctly solved the system of linear equations. From the first equation:
x = 4 - y + z.
The second and third equatins therefore become -3y + z = 6.
Let z = t where t is a free parameter that can equal any real number. Now solve for x and y in terms of t. The a, b, c etc. is simply telling you that your answer will involve fractions. If you do as I have said your answer will be in the required form.
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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October 31st, 2009, 03:59 PM
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Quote:
Originally Posted by sf1903 The question is, Solve the equation! Attachment 13603 I think I have solved the first part...
x = 8
y = -1
z = 3 This is is only one of the solutions: if you write down your augmented matrix, you get after simplifying it (by Gauss's method, say): 
As the third row is clearly a scalar multiple of the 2nd one it will vanish in the next step, and the general solution is  
As you can see, we wrote x,y as functions of z. Now just write  and we're done.
This solution means: for ANY choice of the parameter t, you plug in this choice above for z and thus for x,y and you'll get a solution.
Tonio[/color] But then they say that the answer has to be written as; Attachment 13604 Where a,b,c,d,e,f,g,h have to be itegers.
[color=red] I have absolutely no idea how to solve this problem. Please help! What is... a=? b=?
c=?
d=?
e=?
f=?
g=?
h=?
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