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Exercise - 4.6

Determinants

**Question-1 :-**
Examine the consistency of the system of equations :

x + 2y = 2

2x + 3y = 3

Hence, the given system of equations is consistent.

**Question-2 :-**
Examine the consistency of the system of equations :

2x – y = 5

x + y = 4

Hence, the given system of equations is consistent.

**Question-3 :-**
Examine the consistency of the system of equations :

x + 3y = 5

2x + 6y = 8

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

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

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

Hence, the given system of equations is consistent.

**Question-7 :-**
Solve system of linear equations, using matrix method :

5x + 2y = 4

7x + 3y = 5

**Question-8 :-**
Solve system of linear equations, using matrix method :

2x – y = –2

3x + 4y = 3

**Question-9 :-**
Solve system of linear equations, using matrix method :

4x – 3y = 3

3x – 5y = 7

**Question-10 :-**
Solve system of linear equations, using matrix method :

5x + 2y = 3

3x + 2y = 5

**Question-11 :-**
Solve system of linear equations, using matrix method :

2x + y + z = 1

x – 2y – z = 3/2

3y – 5z = 9

**Question-12 :-**
Solve system of linear equations, using matrix method :

x – y + z = 4

2x + y – 3z = 0

x + y + z = 2

**Question-13 :-**
Solve system of linear equations, using matrix method :

2x + 3y +3 z = 5

x – 2y + z = – 4

3x – y – 2z = 3

**Question-14 :-**
Solve system of linear equations, using matrix method :

x – y + 2z = 7

3x + 4y – 5z = – 5

2x – y + 3z = 12

**Question-15 :-**
find A^{-1}. Using A^{-1} solve the system of equations :

2x – 3y + 5z = 11

3x + 2y – 4z = – 5

x + y – 2z = – 3

**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.

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: 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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