Matrix practice

https://sagecell.sagemath.org/

# 1
print('*** Q1 ***')
A = matrix([[1,2],[3,4]])
b = vector([5,6])
print(A)
print(b)
print('*** A1 ***')
print(A.solve_right(b))

# 2
print('\n*** Q2 ***')
A = matrix([[2,-1,1],[1,0,-1],[3,-1,2]])
b = vector([2,-1,3])
print(A)
print(b)
print('*** A2 ***')
print(A.solve_right(b))

# 3
print('\n*** Q3 ***')
A = matrix([[1,1,1],[0,2,5],[2,5,-1]])
b = vector([6,-4,27])
print(A)
print(b)
print('*** A3 ***')
print(A.solve_right(b))

# 4
print('\n*** Q4 ***')
A = matrix([[1,3,1],[1,1,-1],[3,11,5]])
b = vector([9,1,35])
print(A)
print(b)
print('*** A4 ***')
print(A.solve_right(b))

# 5
print('\n*** Q5 ***')
A = matrix([[1,-2,3],[2,-4,6],[1,1,1]])
b = vector([4,8,3])
print(A)
print(b)
print('*** A5 ***')
# solution process
print('[A⋮b]:')
print(A.augment(b))
print("RREF([A⋮b]):")
print(A.augment(b).rref())
try: print(A.solve_right(b))
except: print('Has no solution.')

# 6
print('\n*** Q6 ***')
A = matrix([[1,2,1],[2,4,-2],[-1,-2,1]])
b = vector([1,2,-1])
print(A)
print(b)
print('*** A6 ***')
# solution process
print('[A⋮b]:')
print(A.augment(b))
print("RREF([A⋮b]):")
print(A.augment(b).rref())
try: print(A.solve_right(b))
except: print('Has no solution.')

# 7
print('\n*** Q7 ***')
A = matrix([[2,4],[1,3]])
b = vector([10,7])
print(A)
print(b)
print('*** A7 ***')
# solution process
print('[A⋮b]:')
print(A.augment(b))
print("RREF([A⋮b]):")
print(A.augment(b).rref())
try: print(A.solve_right(b))
except: print('Has no solution.')

# 8
print('\n*** Q8 ***')
A = matrix([[4,2,-1],[1,5,2],[2,-1,3]])
b = vector([5,12,6])
print(A)
print(b)
print('*** A8 ***')
# solution process
print('[A⋮b]:')
print(A.augment(b))
print("RREF([A⋮b]):")
print(A.augment(b).rref())
try: print(A.solve_right(b))
except: print('Has no solution.')

# 9
print('\n*** Q9 ***')
A = matrix([[1,1,1],[2,2,2],[1,-1,0]])
b = vector([6,12,1])
print(A)
print(b)
print('*** A9 ***')
# solution process
print('[A⋮b]:')
print(A.augment(b))
print("RREF([A⋮b]):")
print(A.augment(b).rref())
try: print(A.solve_right(b))
except: print('Has no solution.')

# 10
print('\n*** Q10 ***')
A = matrix([[1,2,3],[0,1,4],[5,6,0]])
b = vector([7,8,9])
print(A)
print(b)
print('*** A10 ***')
# solution process
print('[A⋮b]:')
print(A.augment(b))
print("RREF([A⋮b]):")
print(A.augment(b).rref())
try: print(A.solve_right(b))
except: print('Has no solution.')