Matrices

 

In Derive

For comparison with other CAS choose from: Axiom Macsyma Maple Mathematica Reduce

x := [[a,b],[c,d]]

           a  b  
    X :=         
           c  d

y := [[u],[v]]

           u  
    Y :=      
           v

det(x)

    DET (X)


    a d - b c

z := x^(-1) . y

          -1
    Z := X     Y


       d u - b v   
      -----------  
       a d - b c   
                   
       a v - c u   
      -----------  
       a d - b c

1/x^2

     1
    ----
      2
     X


                       2                                            
                b c + d                         b (a + d)           
       ---------------------------   - ---------------------------  
         2  2                2  2        2  2                2  2   
        a  d  - 2 a b c d + b  c        a  d  - 2 a b c d + b  c    
                                                                    
                                                2                   
                 c (a + d)                     a  + b c             
      - ---------------------------   ---------------------------   
          2  2                2  2      2  2                2  2    
         a  d  - 2 a b c d + b  c      a  d  - 2 a b c d + b  c

eigenvalues([[2,-1,1],[0,1,1],[-1,1,1]])

                    2  -1  1      
                                  
    EIGENVALUES     0   1  1  , e 
                                  
                   -1   1  1      


    [e = 1, e = 2]