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--- lecture_5_slides [2017/02/03 16:12] – rupert
+++ lecture_5_slides [2017/02/07 10:15] (current) – rupert
@@ Line 1: / Line 1: @@
 ~~REVEAL~~
+===== The story so far... =====
+  * Systems of linear equations
+  * The augmented matrix
+  * Elementary Row Operations (EROs)
+  * Row Echelon Form (REF)
+  * Reduced Row Echelon Form (RREF)
+===== Today =====
+  - How to solve a system in REF or RREF
+  - How to find REF or RREF for a system
 ===== Solving a system in REF or RREF =====
@@ Line 21: / Line 34: @@
 Solve the linear system for $\newcommand{\sm}{\left[\begin{smallmatrix}}\newcommand{\esm}{\end{smallmatrix}\right]} \sm 1&2&3&0&0&8\\0&0&1&1&1&5\\0&0&0&1&3&4\esm$.
+  * Observe: it's in REF
   * Free variables: $x_2$, $x_5$. Set $x_2=s$, $x_5=t$.
     * $ x_4+3x_5=4\implies x_4=4-3x_5=4-3t$
@@ Line 29: / Line 43: @@
 ====== Gaussian elimination ======
-* How to put an augmented matrix into REF or RREF using EROs
+A systematic way to put an augmented matrix into REF or RREF using EROs
   * REF=row echelon form
   * RREF=reduced row echelon form
@@ Line 59: / Line 73: @@
 Use Gaussian elimination to solve the linear system
-\begin{align*} 2x+y+3x+4w&=27\\ x+2y+3z+2w&=30\\x+y+3z+w&=25\end{align*}
+\begin{align*} 2x+y+3z+4w&=27\\ x+2y+3z+2w&=30\\x+y+3z+w&=25\end{align*}
 ==== ====