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Exercise - 4.6

Question-1 :-  Examine the consistency of the system of equations :
x + 2y = 2
2x + 3y = 3

Solution :-
        determinant
  Hence, the given system of equations is consistent.
    

Question-2 :-  Examine the consistency of the system of equations :
2x – y = 5
x + y = 4

Solution :-
        determinant
  Hence, the given system of equations is consistent.
    

Question-3 :-  Examine the consistency of the system of equations :
x + 3y = 5
2x + 6y = 8

Solution :-
        determinant
  Hence, the given system of equations is inconsistent.
    

Question-4 :-  Examine the consistency of the system of equations :
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4

Solution :-
        determinant
  Hence, the given system of equations is consistent.
    

Question-5 :-  Examine the consistency of the system of equations :
3x–y – 2z = 2
2y – z = –1
3x – 5y = 3

Solution :-
        determinant
  Hence, the given system of equations is inconsistent.
    

Question-6 :-  Examine the consistency of the system of equations :
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = –1

Solution :-
        determinant
  Hence, the given system of equations is consistent.
    

Question-7 :-  Solve system of linear equations, using matrix method :
5x + 2y = 4
7x + 3y = 5

Solution :-
        determinant
    

Question-8 :-  Solve system of linear equations, using matrix method :
2x – y = –2
3x + 4y = 3

Solution :-
        determinant
    

Question-9 :-  Solve system of linear equations, using matrix method :
4x – 3y = 3
3x – 5y = 7

Solution :-
        determinant
    

Question-10 :-  Solve system of linear equations, using matrix method :
5x + 2y = 3
3x + 2y = 5

Solution :-
        determinant
    

Question-11 :-  Solve system of linear equations, using matrix method :
2x + y + z = 1
x – 2y – z = 3/2
3y – 5z = 9

Solution :-
        determinant
    

Question-12 :-  Solve system of linear equations, using matrix method :
x – y + z = 4
2x + y – 3z = 0
x + y + z = 2

Solution :-
        determinant
    

Question-13 :-  Solve system of linear equations, using matrix method :
2x + 3y +3 z = 5
x – 2y + z = – 4
3x – y – 2z = 3

Solution :-
        determinant
    

Question-14 :-  Solve system of linear equations, using matrix method :
x – y + 2z = 7
3x + 4y – 5z = – 5
2x – y + 3z = 12

Solution :-
        determinant
    

Question-15 :-  determinant find A-1. Using A-1 solve the system of equations :
2x – 3y + 5z = 11
3x + 2y – 4z = – 5
x + y – 2z = – 3

Solution :-
        determinant
    

Question-16 :-  The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ₹ 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is ₹ 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is ₹ 70. Find cost of each item per kg by matrix method.

Solution :-
  Let the cost of onions, wheat, and rice per kg be ₹ x, ₹ y,and ₹ z respectively.
  Then, the given situation can be represented by a system of equations as:
        determinant
  Hence, the cost of onions is ₹ 5 per kg, the cost of wheat is ₹ 8 per kg, and the cost of rice is ₹ 8 per kg.
    
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