notes

commit 210d6a93e0b09bd9e718a76be1bd28b4078525e8
parent 8b38a4fed496498a81ef7d29404085013fb2af61
Author: AndrewLockVI <andrewlaack1@gmail.com>
Date:   Wed, 22 Jan 2025 08:29:20 -0600

Added scratch work

Diffstat:
A
work/linear-algebra/01-21-2025.md
 | 
34
++++++++++++++++++++++++++++++++++
A
work/linear-algebra/01-22-2025.md
 | 
40
++++++++++++++++++++++++++++++++++++++++

2 files changed, 74 insertions(+), 0 deletions(-)
diff --git a/work/linear-algebra/01-21-2025.md b/work/linear-algebra/01-21-2025.md
@@ -0,0 +1,34 @@
+1.
+
+Gaussian Elimination
+
+1	2	1   |   2
+3	8	1   |   12
+0	4	1   |   2
+
+1	2	1   |   2
+0	2   -2  |   6
+0	4	1   |   2
+
+1	2	1   |   2
+0	2	-2  |   6
+0	0	5   |   -10
+
+c = <2, 6, -10>
+
+
+x + 2y + z = 2
+    2y + -2z = 6
+        5z = -10
+
+z = -2
+y = 1
+x = 2
+
+---
+
+2.
+
+1	2	1   |   2
+3	8	1   |   12
+0	4	1   |   2
diff --git a/work/linear-algebra/01-22-2025.md b/work/linear-algebra/01-22-2025.md
@@ -0,0 +1,40 @@
+[2]             [2 12]
+[3] * [1 6] =   [3 18]
+[4]             [4 24]
+
+ 
+        [2]
+[1 6] * [3] = not possible, size mismatch
+        [4]
+
+
+INVERT THE MATRIX:
+
+A = [1 3]
+    [2 7]
+
+
+A^-1 [1 3] = [1 0]
+     [2 7] = [0 1]
+
+
+[1 3] .. [1 0]
+[2 7]    [0 1]
+
+[1 3] ..  [1 0]
+[0 1]    [-2 1]
+
+[1 0] .. [7 -3]
+[0 1]    [-2 1]
+
+inverse of A is
+
+[7 -3]
+[-2 1]
+
+To verify:
+
+[1 3] * [7 -3] = [7 - 6   -3 + 3] = [1 0]
+[2 7]   [-2 1]   [14 - 14 -6 + 7]   [0 1]
+
+yay...