A=matrix(QQ, 2, 2, [-2, 4, 1, 1]) # input A
print A.charpoly() # characteristic equation of A
print
print solve(x^2 + x - 6==0, x)
print
print A.eigenvalues() # eigenvalues of A
print
print (2*identity_matrix(2)-A).echelon_form() # consider only coefficient matrix
print
print (-3*identity_matrix(2)-A).echelon_form() # consider only coefficient matrix
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x^2 + x - 6
[
x == -3,
x == 2
]
[2, -3]
[ 1 -1]
[ 0 0]
[1 4]
[0 0]
x^2 + x - 6
[
x == -3,
x == 2
]
[2, -3]
[ 1 -1]
[ 0 0]
[1 4]
[0 0]
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