X belongto A, eigenvector(X) = 0

from this statement , 

using linearalgebra package eigenvectors function

the eigenvector matrix [3][1],[3][2],[3][3] are 1 , contradict 1=0

so, need to find another kind of eigenvector in terms of algebra 

using original basic calculation solve, however got error

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);
eigenvector1 := Eigenvectors(m);
solve(
[eigenvector1[2][1][1]=0, eigenvector1[2][1][2]=0, eigenvector1[2][1][3]=0,
eigenvector1[2][2][1]=0, eigenvector1[2][2][2]=0, eigenvector1[2][2][3]=0,
eigenvector1[2][3][1]=0, eigenvector1[2][3][2]=0, eigenvector1[2][3][3]=0]
);

solve(
[eigenvector1[2][1][1]=0, eigenvector1[2][1][2]=0, eigenvector1[2][1][3]=0,
eigenvector1[2][2][1]=0, eigenvector1[2][2][2]=0, eigenvector1[2][2][3]=0]
);

eigenvalue1 :=
(1/6)*(36*a7*a1*a3+108*a7*a2*a6+108*a8*a4*a3+36*a8*a5*a6

...

eigenvalue2 :=
-(1/12)*(36*a7*a1*a3+108*a7*a2*a6+108*a8*a4*a3+36*a8*a5*a6

...

eigenvalue3 :=
-(1/12)*(36*a7*a1*a3+108*a7*a2*a6+

...

solve(MatrixMatrixMultiply(Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]])-Matrix([[eigenvalue1,0,0],[0,eigenvalue1,0],[0,0,eigenvalue1]]), Matrix([[x],[y],[z]])),[x,y,z]);
solve(MatrixMatrixMultiply(Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]])-Matrix([[eigenvalue2,0,0],[0,eigenvalue2,0],[0,0,eigenvalue2]]), Matrix([[x],[y],[z]])),[x,y,z]);
solve(MatrixMatrixMultiply(Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]])-Matrix([[eigenvalue3,0,0],[0,eigenvalue3,0],[0,0,eigenvalue3]]), Matrix([[x],[y],[z]])),[x,y,z]);

got error when using solve

> solve(MatrixMatrixMultiply(Matrix([[a1, a2, a3], [a4, a5, a6], [a7, a8, a9]])-Matrix([[eigenvalue1, 0, 0], [0, eigenvalue1, 0], [0, 0, eigenvalue1]]), Matrix([[x], [y], [z]])), [x, y, z]);
Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({set, list})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received Matrix(3, 1, {(1, 1) = ((2/3)*a1-(1/6)*(36*a7*a1*a3+108*a7*a2*a6+108*a8*a4*a3+36*a8*a6*a5-72*a7*a3*a5-72*a8*a6*a1-72*a9*a4*a2+48*a9*a5*a1-12*a9*a1^2-12*a5*a1^2+8*a1^3-12*a9^2*a1-12*a5^2*a1-12*a9^2*a5-12*a9*a5^2+36*a8*a6*a9+36*a7*a3*a9+36*a4*a2*a1+36*a4*a2*a5+8*a9^3+8*a5^3+12*(54*a7*a2^2*a6*a4*a1+114*a8*a6*a9*a1*a4*a2+6*a8*a6*a9*a1*a7*a3+54*a8*a4*a3^2*a7*a9-60*a9*a1^2*a8*a6*a5-60*a8*a6*a7*a3*a5^2-60*a8*a6*a4*a2*a9^2-24*a9*a1*a4^2*a2^2+6*...

MatrixOperation := module() option package;  export `+`, LinearAlgebra;
    `+` := proc(a::float, b::float) option overload;
 :-`+`(map(x->x^2,a),map(x->x^2,b));
    end proc;
end module;

with(MatrixOperation);
with(LinearAlgebra):
m := Matrix([[1,2],[3,4]]);
L := MatrixMatrixMultiply(m,m);

1 2  1 2
3 4  3 4

1*1+2*3 = 1 + 6 = 1 after overload + with a+b-a*b
1*2+2*4 = 2 + 8 = -6

L should be Matrix([[1, -6],[....]])

 http://en.wikibooks.org/wiki/Linear_Algebra/

Representing_Linear_Maps_with_Matrices

how to calculate the first step

(2,0) -> (1,1,1) and (1,4) -> (1,2,0)

how to use maple command to get (1,1,1) and (1,2,0)

how to use maple command to calculate rep(h)

to get (0,-1/2,1) and (1,-1,0)

http://en.wikibooks.org/wiki/Linear_Algebra

/Representing_Linear_Maps_with_Matrices

> local `+`;
Error, unable to parse

meet difficulty running script in maple 12

restart;  local `+`;  `+`:=proc(a,b) :-`+`(a^`~2`,b^`~2`) end proc;