## Hello Students! In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 4.5**.

You can download the **PDF of NCERT Books Maths Chapter 4** for your easy reference while studying **NCERT Solutions for Maths Class 12 Exercise 4.5**.

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**.

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**

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**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.**

**Using A ^{-1}, solve the following system of linear equations**

**2x – 3y + 5z = 11, **

**3x + 2y – 4z = –5, **

**x + y – 2z = –3**

**Solution:**

**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.

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