NCERT Solutions for Maths Class 12 Exercise 4.5

# NCERT Solutions for Maths Class 12 Exercise 4.5

## NCERT Solutions for Maths Class 12 Exercise 4.5

Examine the consistency of the system of equations in Questions 1 to 6:

### Maths Class 12 Ex 4.5 Question 1.

x + 2y = 2
2x + 3y = 3

Solution:
x + 2y = 2,
2x + 3y = 3
Matrix for the above equations is AX = B.

Hence, the equations are consistent.

### Maths Class 12 Ex 4.5 Question 2.

2x – y = 5
x + y = 4

Solution:

2x – y = 5,
x + y = 4
Matrix for the above equations is AX = B.

Hence, the equations are consistent.

### Maths Class 12 Ex 4.5 Question 3.

x + 3y = 5,
2x + 6y = 8

Solution:
x + 3y = 5,
2x + 6y = 8
Matrix for the above equations is AX = B.

Hence, the equations are inconsistent with no solution.

### Maths Class 12 Ex 4.5 Question 4.

x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4

Solution:
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Matrix for the above equations is AX = B.

Hence, the equations are consistent.

### Maths Class 12 Ex 4.5 Question 5.

3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3

Solution:
3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3
Matrix for the above equations is AX = B.

Hence, the equations are inconsistent with no solution.

### Maths Class 12 Ex 4.5 Question 6.

5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = –1

Solution:
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = –1
Matrix for the above equations is AX = B.

Hence, the equations are consistent with a unique solution.

Solve system of linear equations, using matrix method, in Questions 7 to 14:

### Maths Class 12 Ex 4.5 Question 7.

5x + 2y = 4
7x + 3y = 5

Solution:
The given system of equations can be written as

### Maths Class 12 Ex 4.5 Question 8.

2x – y = – 2
3x + 4y = 3

Solution:
The given system of equations can be written as

### Maths Class 12 Ex 4.5 Question 9.

4x – 3y = 3
3x – 5y = 7

Solution:
The given system of equations can be written as

### Maths Class 12 Ex 4.5 Question 10.

5x + 2y = 3
3x + 2y = 5

Solution:
The given system of equations can be written as

Therefore, x = –1 and y = 4.

### Maths Class 12 Ex 4.5 Question 11.

2x + y + z = 1,
x – 2y – z = 3/2
3y – 5z = 9

Solution:
The given system of equations can be written as

### Maths Class 12 Ex 4.5 Question 12.

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

Solution:
The given system of equations can be written as

Therefore, x = 2, y = –1 and z = 1.

### Maths Class 12 Ex 4.5 Question 13.

2x + 3y + 3z = 5
x – 2y + z = – 4
3x – y – 2z = 3

Solution:
The given system of equations can be written as:

Therefore, x = 1, y = 2 and z = –1.

### Maths Class 12 Ex 4.5 Question 14.

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

Solution:
The given system of equations can be written as

Therefore, x = 2, y = 1 and z = 3.

### Maths Class 12 Ex 4.5 Question 15.

If A = , find A-1.

Using A-1, solve the following system of linear equations

2x – 3y + 5z = 11,

3x + 2y – 4z = –5,

x + y – 2z = –3

Solution:

Therefore, x = 1, y = 2 and z = 3.

### Maths Class 12 Ex 4.5 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 the cost of each item per kg by matrix method.

Solution:
Let the cost of 1 kg onion be  x, the cost of 1 kg wheat be  y and the cost of 1 kg rice be  z. According to the given data, we have the following three equations.
4x + 3y + 2z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70

Matrix from the above equations is AX = B.

Therefore, x = 5, y = 8 and z = 8.

Hence, the cost of onion, wheat and rice per kg are  5,  8 and  8, respectively.