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--- lecture_2 [2015/01/22 10:58] – rupert
+++ lecture_2 [2015/01/22 11:07] (current) – [Linear equations (in general)] rupert
@@ Line 20: / Line 20: @@
 === Example ===
-\[ 3x_1+5x_2-7x_3+11x_4=1\] is a linear equation in 4 variables. A typical solution will be a point $(x_1,x_2,x_3,x_4)\in \mathbb{R}^4$. The set of all solutions is a 3-dimensional object in $\mathbb{R}^4$, called a [[wp>hyperplane]]. Since we can't draw pictures in 4-dimensional space $\mathbb{R^4}$ we can't draw this set of solutions!
+\[ 3x_1+5x_2-7x_3+11x_4=12\] is a linear equation in 4 variables.
+  * A typical solution will be a point $(x_1,x_2,x_3,x_4)\in \mathbb{R}^4$ so that $3x_1+5x_2-7x_3+11x_4$ really does equal $12$.
+  * For example, $(-2,0,-1,1)$ is a solution.
+  * The set of all solutions is a 3-dimensional object in $\mathbb{R}^4$, called a [[wp>hyperplane]].
+  * Since we can't draw pictures in 4-dimensional space $\mathbb{R^4}$ we can't draw this set of solutions!
 ==== Systems of linear equations ====