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--- lecture_14_slides [2017/03/08 17:19] – [Example: using EROs to find the determinant] rupert
+++ lecture_14_slides [2017/03/09 10:45] (current) – [Corollary: the determinant of an upper triangular matrix] rupert
@@ Line 98: / Line 98: @@
 If $A$ is an upper triangular matrix or a diagonal matrix, then the determinant of $A$ is the product of its diagonal entries: \[\det(A)=a_{11}a_{22}\dots a_{nn}.\]
-  * Every upper triangular matrix is diagonal!
+  * Every diagonal matrix is upper triangular!
   * So it suffices just to prove it for upper triangular matrices.
@@ Line 210: / Line 210: @@
 \\&=12\vm{1&3&1&1\\\color{blue}0&\color{blue}{-1}&\color{blue}{-1}&\color{blue}{0}\\\color{blue}0&\color{blue}1&\color{blue}3&\color{blue}2\\0&-4&-1&-0}
 =\color{blue}{-}12\vm{1&3&1&1\\0&\color{green}1&3&2\\0&\color{red}{-1}&{-1}&{0}\\0&\color{red}{-4}&-1&0}
-=-12\vm{1&3&1&1\\0&1&3&2\\0&0&\color{green}2&2\\0&0&\color{red}{11}&8}
+\\&=-12\vm{1&3&1&1\\0&1&3&2\\0&0&\color{green}2&2\\0&0&\color{red}{11}&8}
 =-12\vm{1&3&1&1\\0&1&3&2\\0&0&2&2\\0&0&0&-3}
 \\&=-12(1)(1)(2)(-3)=72.
 \end{align*}