# NCERT Solutions for Class 12 Maths Determinants

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Determinants Exercise 4.6*. This

**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}Maths* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions for Class 12 Maths Determinants Exercise 4.6

Examine the consistency of the system of equations in Exercises 1 to 6.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 1.**

x + 2y = 2

2x + 3y = 3

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Hence, the system of equation is consistent.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 2.**

2x – y = 5

x + y = 4

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Hence, the system of equation is consistent.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 3.**

x + 3y = 5

2x + 6y = 8

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Hence, the system of equation is inconsistent with no solution.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 4.**

x + y + z = 1

2x + 3y + 2z = 2

ax + ay + 2az = 4

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Now, there are two cases:

**Case I**: If |A| = a ≠ 0, then the system of equation is consistent with unique solution.

**Case II**: If |A| = a = 0, then we need to calculate adjA.

Hence, the system of equation is inconsistent with no solutions.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 5.**

3x–y – 2z = 2

2y – z = –1

3x – 5y = 3

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Now, A is a singular matrix. So, we need to calculate adjA.

Hence, the system of equation is inconsistent with no solutions.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 6.**

5x – y + 4z = 5

2x + 3y + 5z = 2

5x – 2y + 6z = –1

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Hence, the system of equation is consistent with unique solutions.

Solve system of linear equations, using matrix method, in Exercises 7 to 14.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 7.**

5x + 2y = 4

7x + 3y = 5

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = 2 and y = -3.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 8.**

2x – y = –2

3x + 4y = 3

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = -5/11 and y = 12/11.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 9.**

4x – 3y = 3

3x – 5y = 7

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = -6/11 and y = -19/11.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 10.**

5x + 2y = 3

3x + 2y = 5

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = -1 and y = 4.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 11.**

2x + y + z = 1

x – 2y – z = 3/2

3y – 5z = 9

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = 1, y = 1/2 and z = -3/2.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 12.**

x – y + z = 4

2x + y – 3z = 0

x + y + z = 2

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = 2, y = -1 and z = 1.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 13.**

2x + 3y +3 z = 5

x – 2y + z = – 4

3x – y – 2z = 3

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = 1, y = 2 and z = 1.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 14.**

x – y + 2z = 7

3x + 4y – 5z = – 5

2x – y + 3z = 12

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

Hence, x = 1, y = 1 and z = 3.

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 15.**

If A = , find A^{–1}. Using A–1 solve the system of equations

2x – 3y + 5z = 11

3x + 2y – 4z = – 5

x + y – 2z = – 3

**NCERT Solutions:**

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

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

**NCERT Solutions for Class 12 Maths Determinants ****Exercise**** 4.6: Ques No 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.

**NCERT Solutions:**

Let the cost of 1 kg onion = Rs. x, the cost of 1 kg wheat = Rs. y, the cost of 1 kg rice = Rs. z.

Then,

4x + 3y + 2z = 60,

2x + 4y + 6z = 90,

6x + 2y + 3z = 70

The system of equation can be written in the form of AX = B, where

Thus, A is non-singular matrix, hence its inverse matrix exist.

Now, the solution of the given equation of system is X = A^{-1}B.

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

Thus, the cost of 1 kg onion = Rs. 5, the cost of 1 kg wheat = Rs. 8, the cost of 1 kg rice = Rs. 8.