From fea35021ef877b538e1e93090fcb3d73ea5f40f0 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Wed, 30 Jan 2019 20:45:15 +1100 Subject: [PATCH 1/1] polynomials - simultaneous equations & linear stuff --- methods/polynomials.md | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/methods/polynomials.md b/methods/polynomials.md index b80ea63..02dc629 100644 --- a/methods/polynomials.md +++ b/methods/polynomials.md @@ -48,3 +48,16 @@ $$=a(x-b)(x-c)^3$$ where - $x$-intercepts at $x=b,c,d,e$ + +## Literal equations + +Equations with multiple pronumerals. Solutions are expressed in terms of pronumerals (parameters)) + +## Simultaneous equations (linear) + +- Unique solution - lines intersect at point +- Infinitely many solutions - lines are equal +- No solution - lines are parallel + +Solving in matrix form - use inverse $A^{-1}= {1 \over {ad-bc}}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}$. $A^{-1}$ exists for infinite solutions or no solutions ($ad-bc=0$), does not exist for unique solutions ($ad-bc \ne 0$). +Or use `det` on CAS. \ No newline at end of file -- 2.43.2