%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  Illustration of inv and eye commands 
%%  Some examples from book
%%  Problem 6, p. 107
%%%%%%%%%%%%%%%%%%%%%%%%%%%

A=[.02 .02 .10;.20 .01 0;.10 .02 .01]

A =

    0.0200    0.0200    0.1000
    0.2000    0.0100         0
    0.1000    0.0200    0.0100

D=[4.5;2;1]

D =

    4.5000
    2.0000
    1.0000

help eye
 EYE Identity matrix.
    EYE(N) is the N-by-N identity matrix.
 
    EYE(M,N) or EYE([M,N]) is an M-by-N matrix with 1's on
    the diagonal and zeros elsewhere.
 
    EYE(SIZE(A)) is the same size as A.
 
    EYE with no arguments is the scalar 1.
 
    EYE(M,N,CLASSNAME) or EYE([M,N],CLASSNAME) is an M-by-N matrix with 1's
    of class CLASSNAME on the diagonal and zeros elsewhere.
 
    Note: The size inputs M and N should be nonnegative integers. 
    Negative integers are treated as 0.
 
    Example:
       x = eye(2,3,'int8');
 
    See also SPEYE, ONES, ZEROS, RAND, RANDN.

    Overloaded methods:
       distributed/eye
       codistributor2dbc/eye
       codistributor1d/eye
       codistributed/eye

I=eye(3)

I =

     1     0     0
     0     1     0
     0     0     1

I-A

ans =

    0.9800   -0.0200   -0.1000
   -0.2000    0.9900         0
   -0.1000   -0.0200    0.9900

help inv
 INV    Matrix inverse.
    INV(X) is the inverse of the square matrix X.
    A warning message is printed if X is badly scaled or
    nearly singular.
 
    See also SLASH, PINV, COND, CONDEST, LSQNONNEG, LSCOV.

    Overloaded methods:
       lti/inv
       idmodel/inv
       uss/inv
       umat/inv
       ufrd/inv
       ndlft/inv
       atom/inv

    Reference page in Help browser
       doc inv

inv(I-A)

ans =

    1.0358    0.0230    0.1046
    0.2092    1.0148    0.0211
    0.1089    0.0228    1.0211

X=inv(I-A)*D

X =

    4.8117
    2.9923
    1.5566

quit