Hi everyone.
I have discovered another way to solve simultaneous equations using matrices.
It's called the Cramer's Rule.
Look at the following example to study how Cramer's Rule is used to solve the simultaneous equations below:-
5x + 3y= −11
2x + 4y = −10
Worked solution
D = det of
5 3
2 4
= 20 − 6 = 14
Dx = det of
−11 3
- 10 4
= −44 + 30 = −14
Dy = det of
5 −11
2 -10
= −50 + 22 = −28
Therefore,
x = Dx/D = −14/ 14 = −1
and y = Dy/D = −28/14 = −2
Now it's your turn to use Cramer's Rule to solve the following simultaneous equations.
- x + 5y = 4
2x + 5y = - 2
Work out D, Dx and Dy and then the solutions x and y. Post these as your comments. You have until 10 Feb to do this.
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38 comments:
http://i26.tinypic.com/2w5w13m.gif
Well done, chun lik.
So, do you appreciate cramer's rule more than the normal matrix method of using inverse?
Cramer's rule is more neat and fast, unlike inverse matrix method which requires more steps.
By the way, do I need to point out what method I'm using during O-Level?
http://www.putpicture.com/links/cramers-rule/
Mrs Goh, i am zi xiang for your information
I got a question, where do you get the -12 in the Dy from your example?
http://img246.imageshack.us/img246/3284/cramerrulekq2.png
My Working.
http://i256.photobucket.com/albums/hh169/Heberocks/CramersRule.jpg
Omg! I just realised i posted a broken link! This is the correct one: http://i256.photobucket.com/albums/hh169/Heberocks/CramersRule.jpg
Sorry about that! :P
OMG! This thing is driving me nuts. Blogger's fault, not my fault! Sorry again! I don't mean to spam!
CLICK HERE FOR MY ANSWER
http://i264.photobucket.com/albums/ii172/rainingdays-/cramerrule1.jpg
http://i257.photobucket.com/albums/hh211/farewellphysics/DONE.jpg
the abpve link is not counted
>> http://i257.photobucket.com/albums/hh211/farewellphysics/DONE.jpg
OH COME ON! WHY CAN'T THIS THING WORK!!!!!!!!!! I M SO SORRY.
http://i257.photobucket.com/albums/hh211/farewellphysics/DONE.jpg
Hi Poh Guek
I cannot get what you sent - it's not in the url that you wrote. Please try again
Guo Wen
I can't get what you sent too.
Please try again
Meilin, Natalie, Dingyi and Jane C, I have viewed your answers. Good work.
Hi zx,
The -12 is an error - sorry, it's supposed to be -11. I have changed it now.
Thanks for alerting me to it.
http://img246.imageshack.us/
img246/3284/cramerrulekq2.png
http://i3.photobucket.com/albums/y82/crazy_gal423/Untitled-3-1.jpg
-x + 5y = 4
2x + 5y = - 2
D = det of
-1 5
2 5
= -5-10 = -15
Dx = det of
4 5
-2 5
= 20 + 10 = 30
Dy = det of
-1 4
2 -2
= 2-8 = -6
Hence,
X= Dx/D = 30/-15 = -2
Y= Dy/D = -6/-15 = 2/5
http://s249.photobucket.com/albums/gg219/yukahagiwara/?action=view¤t=cramersrule.png
http://i256.photobucket.com/albums/hh198/yukihagiwara/cramersrule.png
sorry. this is the correct link
http://i249.photobucket.com/albums/gg219/yukahagiwara/cramersrule.png
http://i252.photobucket.com/albums/hh25/diffany1992/lastscan.jpg
- x + 5y = 4
2x + 5y = - 2
D = det of
-1 5
2 5
= -5 − 10 = -15
Dx = det of
4 5
-2 5
= 20 + 10 = 30
Dy = det of
-1 4
2 -2
= 2- 8 = −6
Therefore,
x = Dx/D = 30/-15 = -2
and y = Dy/D = −6/-15 = 2/5
sorry mrs goh, but because I used microsoft words, there's lots of green and red underlines and when i printscreen it, the picture become like that. Hope you don't mind.
My Work
Erm... I think I do it here better... sorry... oh ya... sorry for my late comments too... =p
D= det of
-1 5
2 5
= (-1x5)-(5x2)
= -5 - 10
= -15
Dx= det of
4 5
-2 5
=(4x5)-(-2x5)
= 20+10
= 30
Dy= det of
-1 4
2 -2
=[(-2)x(-1)]-(4x2)
= 2-8
=-6
Therefore,
x=Dx/D
=30/-15
=-2
and
y=Dy/D
=-6/-15
=2/5
-x + 5y = 4
2x + 5y = -2
D = det of
-1 5
2 5
-5-10 = -15
Dx= det of
5 4
5 -2
-10-20=-30
Dy=det of
-1 4
2 -2
2-8=-6
x= Dx/D=30/-15
=-2
y= Dy/D
=- 6/15
-x + 5y = 4
2x + 5y = -2
D = det of
-1 5
2 5
-5-10 = -15
Dx = det of
4 5
-2 5
20 + 10 = 30
Dy = det of
-1 4
2 -2
2-8 = -6
Therefore
X= Dx/D
= 30/-15
= -2
Y= Dy/D
= -6/-15
= 2/5
-x + 5y = 4
2x + 5y = -2
D = -1 5
2 5
= -5-10
= -15
Dx = 4 5
-2 5
= 20-(-10)
= 30
Dy = -1 4
2 -2
= 2-8
= -6
therefore:
x = Dx / D y = Dy /D
= 30/ -15 = -6/ -15
= -2 = 2 / 5
-x + 5y = 4
2x + 5y = -2
D = -1 5
2 5
= -5-10
= -15
Dx = 4 5
-2 5
= 20-(-10)
= 30
Dy = -1 4
2 -2
= 2-8
= -6
therefore,
x = Dx / D y = Dy /D
= 30/ -15 = -6/ -15
= -2 = 2 / 5
-x + 5y = 4
2x + 5y = -2
solution:
D = det of
-1 5
2 5
->-5-10 = -15
Dx = det of
4 5
-2 5
->20 + 10 = 30
Dy = det of
-1 4
2 -2
->2-8 = -6
Therefore,
X= Dx/D
= 30/-15
= -2
Y= Dy/D
= -6/-15
= 2/5
-x + 5y = 4
2x + 5y = -2
D = det of
-1 5
2 5
-5-10 = -15
Dx = det of
4 5
-2 5
20 + 10 = 30
Dy = det of
-1 4
2 -2
2-8 = -6
Therefore
X= Dx/D
= 30/-15
= -2
Y= Dy/D
= -6/-15
= 2/5
-x + 5y = 4
2x + 5y = -2
D = det of
-1 5
2 5
-5-10 = -15
Dx = det of
4 5
-2 5
20 + 10 = 30
Dy = det of
-1 4
2 -2
2-8 = -6
Therefore
X= Dx/D
= 30/-15
= -2
Y= Dy/D
= -6/-15
= 2/5
o_0 omg. i catch no ball
dun understand at all?so complicated..got simpler rule?
well guys I did a online calculator that solve cramer's rule step by spep, well it works for 3*3 system of equation, I hope this help
www.algebrasolver.totalh.com
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