vault backup: 2026-05-28 00:30:57

Wiki/Math/Matricies/Determinant of a Matrix.md

@@ -1,3 +1,5 @@
+#rs/class/math163 #math 
+- - -
 For a 2 x 2 matrix:
 $$ \det\begin{pmatrix}
 a&b\\c&d
@@ -5,6 +7,15 @@ a&b\\c&d
 For a 3 x 3 matrix:
 $$\begin{vmatrix} a&b&c\\d&e&f\\g&h&i\end{vmatrix} = a\begin{vmatrix} e&f\\h&i\end{vmatrix} - b\begin{vmatrix} d&f\\g&i\end{vmatrix} + c\begin{vmatrix} d&e\\g&h\end{vmatrix} = a(ei-hf)-b(di-gf)+c(dh-ge)$$
 ### Properties
-$$\begin{matrix}
+$$\begin{vmatrix}
 a&b\\a&b
-\end{matrix}$$
+\end{vmatrix} = ab - ba = 0$$
+$$\begin{vmatrix}
+r\cdot a&b\\r \cdot c&d
+\end{vmatrix} = rad - rbc = r(ad - bc) = r \cdot \begin{vmatrix}
+a&b\\c&d
+\end{vmatrix}$$
+
+$$\begin{vmatrix}
+1&0\\0&1
+\end{vmatrix} = 1$$