## NCERT Solutions for Class 12 Maths Chapter 4 – Determinants Ex 4.6

#### Question 1:

Examine the consistency of the system of equations.
+ 2= 2
2x + 3= 3

The given system of equations is:
+ 2= 2
2x + 3= 3
The given system of equations can be written in the form of AX = B, where
∴ A is non-singular.
Therefore, A−1 exists.
Hence, the given system of equations is consistent.

#### Question 2:

Examine the consistency of the system of equations.
2− y = 5
x + = 4

The given system of equations is:
2− y = 5
x + = 4
The given system of equations can be written in the form of AX = B, where
∴ A is non-singular.
Therefore, A−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

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
∴ 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 4:

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

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, A−1 exists.
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

The given system of equations is:
3x − y − 2z = 2
2y − z = −1
3x − 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 − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1

The given system of equations is:
5x − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1
This system of equations can be written in the form of AX = B, where
∴ A is non-singular.
Therefore, A−1 exists.
Hence, the given system of equations is consistent.

#### Question 7:

Solve system of linear equations, using matrix method.

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.

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.

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

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.

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 − y + z = 4
2x + y − 3z = 0
x + y + z = 2

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 − 2y + z = −4
3x − y − 2z = 3

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 − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12

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 A−1. Using A−1 solve the system of equations

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.