m = int(input("enter the number of rows:"))
n = int(input("enter the number of coloum:"))
k = m * n
if k == 4:
a11 = int(input("enter a a11 element in A matrix:"))
a12 = int(input("enter a a12 element in A matrix:"))
a21 = int(input("enter a a21 element in A matrix:"))
a22 = int(input("enter a a22 element in A matrix:"))
s1 = a11 + a22
s2 = a11 * a22 - a21 * a12
s1 = -1 * s1
print("the value of s1:", -1 * s1)
print("the value of s2:", s2)
print("the character equation is :x**2", s1, "x", s2, "=0")
a = 1
b = s1
c = s2
r1 = (b ** 2 - 4 * a * c)
r1 = -b + r1 ** 0.5
r1 = r1 / 2 * a
r2 = (b ** 2 - 4 * a * c)
r2 = -b - r2 ** 0.5
r2 = r2 / 2 * a
roots = [r1, r2]
roots.sort()
print("the eigen values are:", roots)
elif k == 9:
a11 = int(input("enter a a11 element in A matrix:"))
a12 = int(input("enter a a12 element in A matrix:"))
a13 = int(input("enter a a13 element in A matrix:"))
a21 = int(input("enter a a21 element in A matrix:"))
a22 = int(input("enter a a22 element in A matrix:"))
a23 = int(input("enter a a23 element in A matrix:"))
a31 = int(input("enter a a31 element in A matrix:"))
a32 = int(input("enter a a32 element in A matrix:"))
a33 = int(input("enter a a33 element in A matrix:"))
s1 = a11 + a22 + a33
s2 = a22 * a33 - a32 * a23 + a11 * a33 - a31 * a13 + a11 * a22 - a21 * a12
s3 = a11 * (a22 * a33 - a32 * a23) - a12 * (a21 * a33 - a31 * a23) + a13 * (a21 * a32 - a31 * a22)
s1 = -1 * s1
s3 = -1 * s3
print("the value of s1:", -1 * s1)
print("the value of s2:", s2)
print("the value of s3:", -1 * s3)
print("the character equation is :x**3", s1, "x**2", s2, "x", s3, "=0")
n1 = 1
n2 = s1
n3 = s2
n4 = s3
for i in range(-1, 100):
r3 = i + 1
a = n1 + 0
b = a * r3
b = n2 + b
c = b * r3
c = n3 + c
d = c * r3
d = n4 + d
if d == 0:
print(r3)
r1 = (b ** 2 - 4 * a * c)
r1 = -b + r1 ** 0.5
r1 = r1 / 2 * a
r2 = (b ** 2 - 4 * a * c)
r2 = -b - r2 ** 0.5
r2 = r2 / 2 * a
r1 = int(r1)
r2 = int(r2)
r3 = int(r3)
roots = [r1, r2, r3]
roots.sort()
print("the eigen values are:", roots)
break
else:
print(end="")
else:
print("2x2 and 3x3 matrix only exist ")
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