Eliminant/Examples/Arbitrary Example 1
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Example of Eliminant
Consider the system of simultaneous linear equations:
| \(\ds a_1 x + b_1 y + c_1\) | \(=\) | \(\ds 0\) | ||||||||||||
| \(\ds a_2 x + b_2 y + c_2\) | \(=\) | \(\ds 0\) | ||||||||||||
| \(\ds a_3 x + b_3 y + c_3\) | \(=\) | \(\ds 0\) |
The eliminant of the above is:
- $\begin {vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end {vmatrix}$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): eliminant (resultant)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): eliminant (resultant)