# Problem 9:
# 
A = matrix(c(1, complex(real=0, imag=1), complex(real=0, imag=-1), 1), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 10:
# 
A = matrix(c(2, complex(real=2, imag=1), -1, complex(real=-1, imag=-1)), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 11:
# 
A = matrix(c(1, 1, 2,
             1, 2, 1,
             2, 1, 1), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 12:
# 
A = matrix(c(3, 2, 4, 2, 0, 2, 4, 2, 3), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 13:
# 
A = matrix(c(1, 1, 1,
             2, 1, -1,
             -8, -5, -3), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 14:
# 
A = matrix(c(1, -1, 4,
             3, 2, -1,
             2, 1, -1), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 15:
# 
A = matrix(c(5, -1, 3, 1), nrow=2, ncol=2, byrow=T)
print(eigen(A))
A = matrix(c(1, 1, 1, 3), nrow=2, ncol=2, byrow=T)
solve(A, c(2, -1))

# Problem 16:
# 
A = matrix(c(-2, 1, -5, 4), nrow=2, ncol=2, byrow=T)
print(eigen(A))
A = matrix(c(1, 1, 5, 1), nrow=2, ncol=2, byrow=T)
solve(A, c(1, 3))

# Problem 17:
# 
A = matrix(c(1, 1, 2, 0, 2, 2, -1, 1, 3), nrow=3, ncol=3, byrow=T)
print(eigen(A))
A = matrix(c(2, 1, 0, 2, 1, -2, 1, 0, 1), nrow=3, ncol=3, byrow=T)
solve(A, c(2, 0, 1))

# Problem 18:
# 
A = matrix(c(0, 0, -1, 2, 0, 0, -1, 2, 4), nrow=3, ncol=3, byrow=T)
print(eigen(A))
A = matrix(c(-2, -1, 1,
             -1, -2, -2,
             8, 1, 1), nrow=3, ncol=3, byrow=T)
solve(A, c(7, 5, 5))

# Problem 20:
# 
A = matrix(c(2, -1, 3, -2), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 21:
# 
A = matrix(c(5, -1, 3, 1), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 22:
# 
A = matrix(c(4, -3, 8, -6), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 23:
# 
A = matrix(c(3, -2, 2, -2), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 32:
# 
R1 = 1
R2 = 3/5
L = 2
C = 2/3
A = matrix(c(-R1/L, -1/L, 1/C, -1/(C*R2)), nrow=2, ncol=2, byrow=T)
print(eigen(A))