NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.6 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths 4 Determinants Ex 4.6.

- Determinants Class 12 Ex 4.1
- Determinants Class 12 Ex 4.2
- Determinants Class 12 Ex 4.3
- Determinants Class 12 Ex 4.4
- Determinants Class 12 Ex 4.5

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 4 |

Chapter Name |
Determinants |

Exercise |
Ex 4.6 |

Number of Questions Solved |
16 |

Category |
NCERT Solutions |

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

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

**Question 1.**

**x + 2y = 2**

**2x + 3y = 3**

**Solution:**

x + 2y = 2,

2x + 3y = 3

=>

=> AX = B

Now |A| =

= 3 – 4

= – 1 ≠ 0.

Hence, equations are consistent.

**Question 2.**

**2x – y = 5**

**x + y = 4**

**Solution:**

2x – y = 5,

x + y = 4

=>

=> AX = B

Now |A| =

= 2 + 1

= 3 ≠ 0.

Hence, equations are consistent.

**Question 3.**

**x + 3y = 5,**

**2x + 6y = 8**

**Solution:**

x + 3y = 5,

2x + 6y = 8

=>

=> AX = B

Now |A| =

= 6 – 6

= 0.

Hence, equations are consistent with no solution

**Question 4.**

**x + y + z = 1**

**2x + 3y + 2z = 2**

**ax + ay + 2az = 4**

**Solution:**

x + y + z = 1

2x + 3y + 2z = 2

x + y + z =

**Question 5.**

**3x – y – 2z = 2**

**2y – z = – 1**

**3x – 5y = 3**

**Solution:**

=> AX = B

**Question 6.**

**5x – y + 4z = 5**

**2x + 3y + 5z = 2**

**5x – 2y + 6z = -1**

**Solution:**

Given

5x – y + 4z = 5

2x + 3y + 5z = 2

5x – 2y + 6z = -1

= 5(18 + 10)+1(12 – 25)+4(-4-15)

= 140-13-76

= 51 ≠ 0

Hence equations are consistent with a unique

solution.

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

**Question 7.**

**5x + 2y = 4**

**7x + 3y = 5**

**Solution:**

The given system of equations can be written as

**Question 8.**

**2x – y = – 2**

**3x + 3y = 3**

**Solution:**

The given system of equations can be written

**Question 9.**

**4x – 3y = 3**

**3x – 5y = 7**

**Solution:**

The given system of equations can be written as

where

**Question 10.**

**5x + 2y = 3**

**3x + 2y = 5**

**Solution:**

The given system of equations can be written as

where

**Question 11.**

**2x + y + z = 1,**

**x – 2y – z = 3/2**

**3y – 5z = 9**

**Solution:**

The given system of equations are

2x + y + z = 1,

x – 2y – z = 3/2,

3y – 5z = 9

We know AX = B => X = A^{-1}B

**Question 12.**

**x – y + z = 4**

**2x + y – 3z = 0**

**x + y + z = 2.**

**Solution:**

The given system of equations can be written

**Question 13.**

**2x + 3y + 3z = 5**

**x – 2y + z = – 4**

**3x – y – 2z = 3**

**Solution:**

The given system of equations can be written as:

**Question 14.**

**x – y + 2z = 7**

**3x + 4y – 5z = – 5**

**2x – y + 3z = 12.**

**Solution:**

The given system of equations can be written

**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:**

We have AX = B

where

**Question 16.**

**The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 69. 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 cost of 1 kg onion = Rs x

and cost of 1 kg wheat = Rs y

and cost of 1 kg rice = Rs z

4x+3y+2z=60

2x+4y+6z=90

6x+2y+3z=70

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