NCERT Solutions for Maths Class 12 Exercise 4.6

NCERT Solutions for Maths Class 12 Exercise 4.6

                                                                                                                    NCERT Solutions for Maths Class 12 Exercise 4.6


Hello Students! Welcome to maths-formula.com. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 4.6.

 

You can download the PDF of NCERT Books Maths Chapter 4 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 4.6.

 

Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

 

NCERT Solutions for Maths Class 12 Exercise 4.6 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

 

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

 

NCERT Solutions for Maths Class 12 Exercise 4.6 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

 

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.


NCERT Solutions for Maths Class 12 Exercise 4.1

NCERT Solutions for Maths Class 12 Exercise 4.2

NCERT Solutions for Maths Class 12 Exercise 4.3

NCERT Solutions for Maths Class 12 Exercise 4.4

NCERT Solutions for Maths Class 12 Exercise 4.5


NCERT Solutions for Maths Class 12 Exercise 4.6

 

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

Maths Class 12 Ex 4.6 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 4.6 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 4.6 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 4.6 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 4.6 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 4.6 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 4.6 Question 7.

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

Solution:
The given system of equations can be written as


Maths Class 12 Ex 4.6 Question 8.

2x – y = – 2
3x + 4y = 3

Solution:
The given system of equations can be written as


Maths Class 12 Ex 4.6 Question 9.

4x – 3y = 3
3x – 5y = 7

Solution:
The given system of equations can be written as


Maths Class 12 Ex 4.6 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 4.6 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 4.6 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 4.6 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 4.6 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 4.6 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 4.6 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 the cost of each item per kg by matrix method.

Solution:
Let the cost of 1 kg onion be Rs x, the cost of 1 kg wheat be Rs y and the cost of 1 kg rice be Rs 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 Rs. 5, Rs. 8 and Rs. 8, respectively.

NCERT Solutions for Maths Class 12 Exercise 4.1

NCERT Solutions for Maths Class 12 Exercise 4.2

NCERT Solutions for Maths Class 12 Exercise 4.3

NCERT Solutions for Maths Class 12 Exercise 4.4

NCERT Solutions for Maths Class 12 Exercise 4.5

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