Linear Algebra with Sage
<Cofactor Expansion>
Made by SKKU Linear Algebra Lab (2011)
Find a determinant of the matrix @@ \begin{bmatrix} 1 & 1 & 2\\ 2 & 4 & -3\\ 3 & 6 & -5 \end{bmatrix} @@ using a cofactor expansion.
<Cofactor Expansion>
@@ |A|= \sum_{i=1}^n a_{ij}A_{ij} = \sum_{i=1}^n (-1)^{i+j} a_{ij} | A(i | j)|@@ @@(1\leq j \leq n)@@
,where @@A(i | j)@@ is a submatrix obtained from @@A@@ by deleting @@i@@-row and @@j@@-column.
Define a matrix @@A@@ (행렬@@A@@ 생성 및 확인)
A=matrix([[1,1,2],[2,4,-3],[3,6,-5]]); A |
[ 1 1 2]
[ 2 4 -3]
[ 3 6 -5]
Find a cofactor @@ A_{11} = (-1)^{1+1} A(1|1)@@ (@@a_{11}@@의 여인자(Cofactor) @@A_{11}@@을 구한다.)