vault backup: 2026-10-07 09:52:59

College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.1 - Lines and Linear Equations.md

@@ -0,0 +1,25 @@
+#uw/notes #uw/class/math208
+- - -
+- Possible intersections of 3 planes in 3D space
+	- 1 point - one solution
+		- $z=0$
+		- $x=0$
+		- $y=0$
+	- 1 line - infinite solutions
+		- $z=0$
+		- $x=0$
+		- $x=z$
+	- 3 lines - no solutions
+		- $z=0$
+		  $z=x+1$
+		- $z=1-x$
+	- one plane - infinite solutions
+		- $z=0$
+		- $2z=0$
+		- $3z=0$
+	- no intersections - no solutions
+		- $z=0$
+		- $z=1$
+		- $z=2$
+- Adding constant multiple of one linear equation in system does not change solution set of system
+	- concept behind gaussian elimination