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

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

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

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

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

# Problem 6:
# 
A = matrix(c(0, 1, 1,
             1, 0, 1,
             1, 1, 0), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 7:
# 
A = matrix(c(1, -4,
             4, -7), nrow=2, ncol=2, byrow=T)
print(eigen(A))

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

# Problem 9:
# 
A = matrix(c(2, 3/2,
             -3/2, -1), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 10:
# 
A = matrix(c(3, 9,
             -1, -3), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 11:
# 
A = matrix(c(1, 0, 0,
             -4, 1, 0,
             3, 6, 2), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 12:
# 
A = matrix(c(-5/2, 1, 1,
             1, -5/2, 1,
             1, 1, -5/2), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 13:
# 
A = matrix(c(3, -4,
             1, -1), nrow=2, ncol=2, byrow=T)
print(eigen(A))

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

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

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

# Problem 19:
# 
A = matrix(c(5, -3, -2,
             8, -5, -4,
             -4, 3, 3), nrow=3, ncol=3, byrow=T)
print(eigen(A))