Math Is Fun Forum

CoRRupt3d

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I need help with trying to prove Cramer's Rule.

Cramer's Rule states that in the system of equation ax+by=e and cx+dy=f,
    |e  b|            |a  e|
    |f   d|            |c   f|
x=------- and y=-------
    |a  b|            |a  b|
    |c  d|            |c  d|

I'm not sure how to prove this! Help me! D:

Bob

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Registered: 2010-06-20

Posts: 10,140

Re: Click Me! <---Click it!!!

hi CoRRupt3d

Welcome to the forum.

Start by trying to solve this pair using a simultaneous technique:

multiply first by d and second by b

and

subtract

If you factorise the x out and rewrite the expressions as determinants of matrices you have the first formula.  The other is obtained similarly.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

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Re: Click Me! <---Click it!!!

We need to change the subject line

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.