Example 1: Solve the system .

> A:=matrix(2,2,[-3,sqrt(2),sqrt(2),-2]);

> eigenvals(A);

To find eigenvectors we need the column vector and the identity matrix . Notice below how we defined .

> t:=matrix(2,1,[t1,t2]);

> E:=array(1..2,1..2,identity);

We obtain eigenvectors for the egenvalue -1 by solving the system

.

> multiply(A+E,t);

> solve(-2*t1+2^(1/2)*t2=0,t2);

Hence all eigenvectors of the eigenvalue -1 are of the form .We repeat the same procedure for the eigenvalue -4.

> multiply(A+4*E,t);

> solve(t1+2^(1/2)*t2=0,t2)font color=#FF0000>solve(t1+2^(1/2)*t2=0,t2);

Hence all eigenvectors of the eigenvalue -4 are of the form .

Since the eigenvalues are disitinct by setting t1=1 we obtain two independent eigenvectors and .Hence two independent solutions of the system are and .