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

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

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

# Problem 4:
# 
A = matrix(c(2, -5/2,
             9/5, -1), nrow=2, ncol=2, byrow=T)
print(eigen(A))

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

# Problem 6:
# 
A = matrix(c(1, 2,
             -5, -1), nrow=2, ncol=2, byrow=T)
print(eigen(A))

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

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

# Problem 9:
# 
A = matrix(c(1, -5,
             1, -3), nrow=2, ncol=2, byrow=T)
print(eigen(A))

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

# Problem 11:
# 
A = matrix(c(3/4, -2, 
             1, -5/4), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 12:
# 
A = matrix(c(-4/5, 2,
             -1, 6/5), nrow=2, ncol=2, byrow=T)
print(eigen(A))

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

# Problem 22:
# 
A = matrix(c(2, -5, 
             1, -2), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 23:
# 
A = matrix(c(-1/4, 1, 0,
             -1, -1/4, 0,
             0, 0, -1/4), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 24:
# 
A = matrix(c(-1/4, 1, 0,
             -1, -1/4, 0,
             0, 0, 1/10), nrow=3, ncol=3, byrow=T)
print(eigen(A))

# Problem 25:
# 
A = matrix(c(-1/2, -1/8,
             2, -1/2), nrow=2, ncol=2, byrow=T)
print(eigen(A))

# Problem 29:
# 
A = matrix(c(-2, 3/2,
             4/3, -3), nrow=2, ncol=2, byrow=T)
print(eigen(A))


# Problem 30:
# 
A = matrix(c(8, 8, 0, 8,
             0, -6, 0, -6,
             -20, 0, -20, 0,
             15, 8, 15, 0), nrow=4, ncol=4, byrow=T)
print(solve(A, c(2, 1, 0, 0)))