Classroom License -- for classroom instructional use only.

A =[ 1 2 3; 2 3 4; 1,0, 3]

A =

     1     2     3
     2     3     4
     1     0     3

A'

ans =

     1     2     1
     2     3     0
     3     4     3

x=[1 , 2, 3]

x =

     1     2     3

A*x
{Error using <a href="matlab:matlab.internal.language.introspective.errorDocCallback('mtimes')" style="font-weight:bold"> * </a>
Inner matrix dimensions must agree.
} 
A*x'

ans =

    14
    20
    10

A^4*x'

ans =

        2576
        3992
        1120

eigs(A)

ans =

   -0.3723
    2.0000
    5.3723

doc eigs
[V,D]=eigs(A)

V =

    0.9341   -0.4082    0.5276
   -0.2254   -0.8165    0.8198
   -0.2770    0.4082    0.2224


D =

   -0.3723         0         0
         0    2.0000         0
         0         0    5.3723

diag(D)

ans =

   -0.3723
    2.0000
    5.3723

A*V(:,1)

ans =

   -0.3477
    0.0839
    0.1031

D(1,1)*V(:,1)

ans =

   -0.3477
    0.0839
    0.1031

exit