From 12ddf5859fd7cf48b20d60590f76bd70a2eb04a6 Mon Sep 17 00:00:00 2001
From: Daniel Bulant <danbulant@gmail.com>
Date: Mon, 9 May 2022 17:50:54 +0200
Subject: [PATCH] vault backup: 2022-05-09 17:50:54

---
 .../obsidian-activity-history/data.json       |   4 +-
 notes/mat/Rovnice/Matice.md                   | 118 +++++++++++++++++-
 2 files changed, 119 insertions(+), 3 deletions(-)

diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json
index 0bfb539..efa9c71 100644
--- a/notes/.obsidian/plugins/obsidian-activity-history/data.json
+++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json
@@ -13,7 +13,7 @@
     {
       "path": "/",
       "date": "2022-05-09",
-      "size": 835613
+      "size": 837000
     }
   ],
   "activityHistory": [
@@ -642,7 +642,7 @@
         },
         {
           "date": "2022-05-09",
-          "value": 995
+          "value": 2382
         }
       ]
     }
diff --git a/notes/mat/Rovnice/Matice.md b/notes/mat/Rovnice/Matice.md
index 8b9db6c..94b10d7 100644
--- a/notes/mat/Rovnice/Matice.md
+++ b/notes/mat/Rovnice/Matice.md
@@ -27,4 +27,120 @@ Nepočítá se.
 Počet nenulových řádků v matici.
 ## Determinant
 U matice se sečtou násobky diagonal (xyz..) a odečtou násobky opačných diagonál (...zyx).
-Pokud je hodnota 0, je rovnice singulární (nekonečně mnoho řešení, nebo žádné)
\ No newline at end of file
+Pokud je hodnota 0, je rovnice singulární (nekonečně mnoho řešení, nebo žádné)
+
+---
+
+$3x-3y-z=1$
+$x+y+z=1$
+$x-3y-2z=1$
+
+$det A = -2$
+$det A_x = -4$
+$det A_y=-6$
+$det A_z=8$
+
+$x=\frac{det A_x}{det A}=\frac{-4}{-2}=8$
+$y=\frac{det A_y}{det A}=\frac{-6}{-2}=3$
+$z=\frac{det A_z}{det A}=\frac{8}{-2}=-4$
+
+---
+
+$2a-3b+c-d=4$
+$a+3b+2c+3d=2$
+$a+b-2c+d=4$
+$-a+2b-3c+2d=2$
+
+$det A=-44$
+$det A_a=-76$
+$det A_b=44$
+$det A_c=36$
+$det A_d=-72$
+
+$a=\frac{19}{11}$
+$b=-1$
+$c=-\frac9{11}$
+$d=\frac{18}{11}$
+
+
+---
+
+$2x-3y=1$
+$-4x+7y=1$
+
+$4x-6y=2$
+$-4x+7y=1$
+
+$y=3$
+
+$-4x+7*3=1$
+$-4x+21=1$
+$-4x=-20$
+$x=5$
+
+---
+
+$x(x-3)(x+2)=0$
+
+$x^3-3x^2+2x^2-6x=0$
+$x^3-1x^2-6x=0$
+$x_1=0$
+$x_2 = 3$
+$x_3=2$
+
+$K=[0;3;2]$
+
+---
+
+$(x+3)(x^2-3)=0$
+
+$x+3=0$
+$x_1=-3$
+$x^2-3=0$
+$x_2=\sqrt{3}$
+
+$K=[-3;\sqrt{3}]$
+
+---
+
+$\frac{x^2-5}{x+\sqrt{5}}=0$
+$x^2-5=0$
+$x_1=\sqrt{5}$
+$x_2=-\sqrt5$
+$[x\neq-\sqrt5]$
+
+$K=[\sqrt5]$
+
+---
+
+$\frac{x^2-25}{x-5}=3$
+$x^2-25=3x-15$
+$x^2-3x-10=0$
+$[x\neq5]$
+$D=9-4*1*(-10)=49$
+$x_1=\frac{3+7}2=5$
+$x_2=\frac{3-7}2=-2$
+$K=[-2]$
+
+---
+
+$(3x+5)(2-2x)\ge 0$
+
+$3x+5\ge0$ => $x\ge-\frac53$
+$3-2x\ge0$ =>$x\le\frac32$
+$3x+5\le0$ => $x\le-\frac53$
+$3-2x\le0$ =>$x\ge\frac32$
+
+$x\in\lt-\frac53;\frac32\gt$
+$K=\{-\frac53\le x\le\frac32\}$
+
+---
+$(2x-3)(3+2x)\le0$
+
+$2x-3\le0$
+$3+2x\ge0$
+$2x-3\ge0$
+$3+2x\le0$
+
+$x\in\lt\frac32;\frac32\gt$
+$K=\{-\frac32\le x \le \frac32\}$