Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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George,Y
2006-04-07 10:44:25

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
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| = k|
|
|
|= - |
| = |
|

Vandermonde Determinant

George,Y
2006-04-05 16:05:07

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

RauLiTo
2006-04-05 02:47:02

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

George,Y
2006-04-05 00:56:56

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

RauLiTo
2006-04-05 00:07:24

| 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