Math Is Fun Forum

RauLiTo

Member

From: Bahrain

Registered: 2006-01-11

Posts: 142

a question in the DETERMINANTS

| X   X²   1 +X³ |
| Y   Y²   1+Y³   | = 0             
| Z   Z ²  1+Z³  |

that was given ...

prove that X Y Z = -1

help please guys i have an exam tomorrow

Last edited by RauLiTo (2006-04-04 02:08:19)

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ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: a question in the DETERMINANTS

decompenent the last colume, and reform
| X   X²   1 +X³ |                |1  X   X² |      |1  X   X²|
| Y   Y²   1+Y³   | = -1(- 1)| 1  Y   Y² | +XYZ| 1  Y   Y²| = (1+XYZ)VD 
| Z   Z ²  1+Z³  |                |1  Z   Z ²|         | 1  Z   Z ²|

VD -Vander monde Determinant
if x≠ y≠ z
xyz=-1

Last edited by George,Y (2006-04-04 02:57:31)

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X'(y-Xβ)=0

RauLiTo

Member

From: Bahrain

Registered: 2006-01-11

Posts: 142

Re: a question in the DETERMINANTS

thank you very much ... but unfortunately i dind't understand it well ... can someone explain it for me ? !

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ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: a question in the DETERMINANTS

Reread the determinant properties, and then you will understand
|column1 column2 column3a+column3b|
=|column1 column2 column3a|+|column1 column2 column3b|

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X'(y-Xβ)=0

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: a question in the DETERMINANTS

Sorry you may not find these properties in your text book
|a  b  c|  |a  b' c|    |a  b+b'  c|
|d  e  f|+|d  e'  f| = |d  e+e'  f|
|g  h  i|   |g  h'  i|     |g  h+h'  i|
see the bottom of this link

other properties used
|

| = k|

|
|

|= - |

| = |

|

Vandermonde Determinant
 
this link

Last edited by George,Y (2006-04-06 12:52:48)

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X'(y-Xβ)=0