[Linear Algebra] #07 Second and Third order determinants

1. Determinant of second-order

 

D = det(A) = |A|

 

    = $\begin{vmatrix} a_{11} & a_{12}\cr b_{11} & b_{12} \end{vmatrix}$

 

 

· Cramer's rules for the 2 x 2 matrix equation

 

 

 

 

2. Determinant of third-order

 

 

· Cramer's rules for the 3 x 3 matrix equation

 

 

 

 

3. Fundamental Subspaces

 

m : #식   n : #변수

· Col(A) : Column space (image) in $R^m$

· Row(A) : Row space (coimage) in $R^n$

· Null(A) : Null space (kernel) in $R^n$

* Null($A^T$) : Left null space (cokernel) in $R^m$