matrix.out

>> a = [3 2 -1; -1 3 2; 1 -1 -1]                 % 'a' 3X3 coeff matrix

a =
     3     2    -1
    -1     3     2
     1    -1    -1

>> b = [ 10; 5; -1]				 % 'b' RHS (load) vector

b =
    10
     5
    -1

>> x = a\b                                       % from a * x = b, solve for x

x =
   -2.0000
    5.0000
   -6.0000

>> a*x                                           % check that a * x = b

ans =
   10.0000
    5.0000
   -1.0000

>> inva = inv(a)                                 % determine inverse of 'a'

inva =
   -1.0000    3.0000    7.0000
    1.0000   -2.0000   -5.0000
   -2.0000    5.0000   11.0000

>> inva * a                                      % check that inva * a = [I]

ans =
    1.0000    0.0000    0.0000
    0.0000    1.0000    0.0000
    0.0000    0.0000    1.0000

>> inva * b                                      % show that inva * b = x

ans =
   -2.0000
    5.0000
   -6.0000

>> a'                                            % transpose of 'a'

ans =
     3    -1     1
     2     3    -1
    -1     2    -1

>> cond(a)                                       % condition number of 'a'

ans =
   63.0547