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# NCERT Solutions - Determinants, Exercise 4.6 JEE Notes | EduRev

## JEE : NCERT Solutions - Determinants, Exercise 4.6 JEE Notes | EduRev

The document NCERT Solutions - Determinants, Exercise 4.6 JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Determinants

Exercise 4.6

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

Answer
The given system of equations is:
x + 2y = 2
2x + 3y = 3
The given system of equations can be written in the form of AX = B, where

A is non-singular.
Therefore, Aâˆ’1 exists.
Hence, the given system of equations is consistent.

Question 2: Examine the consistency of the system of equations.
2x âˆ’ y = 5 x
+ y = 4

Answer
The given system of equations is:
2x âˆ’ y = 5 x
+ y = 4
The given system of equations can be written in the form of AX = B, where

A is non-singular.
Therefore, Aâˆ’1 exists.
Hence, the given system of equations is consistent.

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

Answer
The given system of equations is:
x + 3y = 5
2x + 6y = 8
The given system of equations can be written in the form of AX = B, where

Thus, the solution of the given system of equations does not exist. Hence, the 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

Answer
The given system of equations is:
x + y + z = 1 2x
+ 3y + 2z = 2 ax
+ ay + 2az = 4
This system of equations can be written in the form AX = B, where

A is non-singular.
Therefore, Aâˆ’1 exists.
Hence, the given system of equations is consistent.

Question 5: Examine the consistency of the system of equations.
3x âˆ’ y âˆ’ 2z = 2
2y âˆ’ z = âˆ’1
3x âˆ’ 5y = 3

Answer
The given system of equations is:
3x âˆ’ y âˆ’ 2z = 2
2y âˆ’ z = âˆ’1
3x âˆ’ 5y = 3
This system of equations can be written in the form of AX = B, where

A is a singular matrix.

Thus, the solution of the given system of equations does not exist. Hence, the system of equations is inconsistent.

Question 6: Examine the consistency of the system of equations.
5x âˆ’ y + 4z = 5
2x + 3y + 5z = 2
5x âˆ’ 2y + 6z = âˆ’1

Answer
The given system of equations is:
5x âˆ’ y + 4z = 5
2x + 3y + 5z = 2
5x âˆ’ 2y + 6z = âˆ’1
This system of equations can be written in the form of AX = B, where

Therefore, Aâˆ’1 exists.
Hence, the given system of equations is consistent.

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

Answer
The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

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

Answer :The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

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

Answer The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

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

Answer: The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

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

Answer: The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

Question 12: Solve system of linear equations, using matrix method.
x âˆ’ y + z = 4

2x + y âˆ’ 3z = 0

x + y + z = 2

Answer: The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

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

Answer: The given system of equations can be written in the form AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

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

x âˆ’ y + 2z = 7
3x + 4y âˆ’ 5z = âˆ’5
2x âˆ’ y + 3z = 12

Answer: The given system of equations can be written in the form of AX = B, where

Thus, A is non-singular. Therefore, its inverse exists.

Question 15:

If
find Aâˆ’1. Using Aâˆ’1 solve the system of equations

Answer

Now, the given system of equations can be written in the form of AX = B, where

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

Answer
Let the cost of onions, wheat, and rice per kg be Rs x, Rs y,and Rs z respectively.
Then, the given situation can be represented by a system of equations as:

This system of equations can be written in the form of AX = B, where

Now,
X = Aâˆ’1 B

Hence, the cost of onions is Rs 5 per kg, the cost of wheat is Rs 8 per kg, and the cost of rice is Rs 8 per kg.

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## Mathematics (Maths) Class 12

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