Determiants

Determiants

1. 2x2

   • |A|=a11a22-a12a21

2. nxn

   • i row: |A|=ai1+.....+aincin
     • j column: |A|=a1jc1j+....+anjcnj
     • Cij=(-1)^i+j(Mij)

3. 3x3

4. nxn

   • lower or upper traingular
     • |A|=product of main daigonal

5. |cA|=c^n(|A|)

   • |BA|=|A||B|
     • |A^t|=|A|
       • |A^-1|=1/|A|
         • |A+B|!=|A|+|B|

6. adj(A)=traspose of cofactor matrix

   • use formla: A^-1=(1/|A|)adj(A)

7. |A|!=0 =>unique suoltion

   • |A|=0 =>no or many soltion

8. cramer rule "|A|!=0"

   • استبدل كل مره عامود بعامود الثوابت
     • x1=|A1|/|A|, x2=|A2|/|A|,...

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