ans  =
 
    1.  
 
-->A=[.8 .3; .2 .7]
 A  =
 
    0.8    0.3  
    0.2    0.7  
 
-->X=[1;0]
 X  =
 
    1.  
    0.  
 
-->for i=1:100, X=A*X; end
 
-->X
 X  =
 
    0.6  
    0.4  
 
-->A*X
 ans  =
 
    0.6  
    0.4  
 
-->help eigenvalue
 
-->spec(A)
 ans  =
 
    1.   
    0.5  
 
-->A=[2 3 1; 4 7 5; 0 -2 2]
 A  =
 
    2.    3.    1.  
    4.    7.    5.  
    0.  - 2.    2.  
 
-->b=[8; 20; 0]
 b  =
 
    8.   
    20.  
    0.   
 
-->C=[A b]
 C  =
 
    2.    3.    1.    8.   
    4.    7.    5.    20.  
    0.  - 2.    2.    0.   
 
-->rref(C)
 ans  =
 
    1.    0.    0.    2.  
    0.    1.    0.    1.  
    0.    0.    1.    1.  
 
-->A = [ 1 2  3; 4 5 6; 7 8 9]
 A  =
 
    1.    2.    3.  
    4.    5.    6.  
    7.    8.    9.  
 
-->E=eye(3,3)
 E  =
 
    1.    0.    0.  
    0.    1.    0.  
    0.    0.    1.  
 
-->E(1,1)=0; E(2,2)=0 ; E(1,2)=1; E(2,1)=1
 E  =
 
    0.    1.    0.  
    1.    0.    0.  
    0.    0.    1.  
 
-->E*A
 ans  =
 
    4.    5.    6.  
    1.    2.    3.  
    7.    8.    9.  
 
-->E=eye(3,3)
 E  =
 
    1.    0.    0.  
    0.    1.    0.  
    0.    0.    1.  
 
-->E(2,2)=3
 E  =
 
    1.    0.    0.  
    0.    3.    0.  
    0.    0.    1.  
 
-->E*A
 ans  =
 
    1.     2.     3.   
    12.    15.    18.  
    7.     8.     9.   
 
-->A
 A  =
 
    1.    2.    3.  
    4.    5.    6.  
    7.    8.    9.  
 
-->E=eye(3,3); E(1,3)=-4
 E  =
 
    1.    0.  - 4.  
    0.    1.    0.  
    0.    0.    1.  
 
-->E*A
 ans  =
 
  - 27.  - 30.  - 33.  
    4.     5.     6.   
    7.     8.     9.   
 
-->E=eye(3,3); E(3,1)=-4
 E  =
 
    1.    0.    0.  
    0.    1.    0.  
  - 4.    0.    1.  
 
-->E*A
 ans  =
 
    1.    2.    3.  
    4.    5.    6.  
    3.    0.  - 3.  
 
-->E=[1 0 0; -1 1 0; 0 0 1]
 E  =
 
    1.    0.    0.  
  - 1.    1.    0.  
    0.    0.    1.  
 
-->A=[ 1 1 1; 1 -1 1; 2 1 2]
 A  =
 
    1.    1.    1.  
    1.  - 1.    1.  
    2.    1.    2.  
 
-->b=10 ; 3 7]
            !--error 276 
Missing operator, comma, or semicolon.

 
 
-->b=[10 ; 3 7]
            !--error 6 
Inconsistent row/column dimensions.

 
 
-->b=[10 ; 3; 7]
 b  =
 
    10.  
    3.   
    7.   
 
-->E*A
 ans  =
 
    1.    1.    1.  
    0.  - 2.    0.  
    2.    1.    2.  
 
-->C=[A b]
 C  =
 
    1.    1.    1.    10.  
    1.  - 1.    1.    3.   
    2.    1.    2.    7.   
 
-->E*C
 ans  =
 
    1.    1.    1.    10.  
    0.  - 2.    0.  - 7.   
    2.    1.    2.    7.   
 
-->E(3,1)=-2
 E  =
 
    1.    0.    0.  
  - 1.    1.    0.  
  - 2.    0.    1.  
 
-->E*C
 ans  =
 
    1.    1.    1.    10.  
    0.  - 2.    0.  - 7.   
    0.  - 1.    0.  - 13.  
 
-->A
 A  =
 
    1.    1.    1.  
    1.  - 1.    1.  
    2.    1.    2.  
 
-->B=[A eye(3,3)]
 B  =
 
    1.    1.    1.    1.    0.    0.  
    1.  - 1.    1.    0.    1.    0.  
    2.    1.    2.    0.    0.    1.  
 
-->rref(B)
 ans  =
 
 
         column 1 to 5
 
    1.    0.    1.    0.    0.3333333  
    0.    1.    0.    0.  - 0.6666667  
    0.    0.    0.    1.    0.3333333  
 
         column 6
 
    0.3333333  
    0.3333333  
  - 0.6666667  
 
-->inv(A)
       !--error 19 
Problem is singular.

 
 
-->A(3,1)=0
 A  =
 
    1.    1.    1.  
    1.  - 1.    1.  
    0.    1.    2.  
 
-->inv(A)
 ans  =
 
    0.75    0.25  - 0.5  
    0.5   - 0.5     0.   
  - 0.25    0.25    0.5  
 
-->B=[A eye(3,3)]
 B  =
 
    1.    1.    1.    1.    0.    0.  
    1.  - 1.    1.    0.    1.    0.  
    0.    1.    2.    0.    0.    1.  
 
-->rref(B)
 ans  =
 
    1.    0.    0.    0.75    0.25  - 0.5  
    0.    1.    0.    0.5   - 0.5     0.   
    0.    0.    1.  - 0.25    0.25    0.5  
 
-->X=[ 1 2 3 ; 4 5 6]
 X  =
 
    1.    2.    3.  
    4.    5.    6.  
 
-->X*X
    !--error 10 
Inconsistent multiplication.

 
 
-->diary(0)