Computing Eigenvalues and Eigenvalues with CoCalc/SageMath

These commands will help you compute eigenvalues and bases of eigenspaces.

c = var('c')
A = matrix(3,3,[8,10,-18,1,3,-2,4,6,-9])
p = expand((A-c).determinant())
print(factor(p))
print(solve(p==0,c))
#Here is the matrix for computing the 2 eigenspace
B = A - 2
print(B)
print(B.rref())
#Here is the matrix for computing the -1 eigenspace
C = A - (-1)
print(C)
print(C.rref())
#Here is the matrix for computing the 1 eigenspace
D = A - 1
print(D)
print(D.rref())

To deal with complex eigenvalues, use the symbol capital I in CoCalc  (SageMath) to represent the complex number i.

CoCalc/SageMath:

c = var('c')
A = matrix(2,2,[1,5,-5,1])
p = expand((A-c).determinant())
print(solve(p==0,c))
print((A - (1+5*I)).rref())