NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths 4 Determinants Ex 4.2.

- Determinants Class 12 Ex 4.1
- Determinants Class 12 Ex 4.3
- Determinants Class 12 Ex 4.4
- Determinants Class 12 Ex 4.5
- Determinants Class 12 Ex 4.6

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 4 |

Chapter Name |
Determinants |

Exercise |
Ex 4.2 |

Number of Questions Solved |
16 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2

**Using the property of determinants and without expanding in Q 1 to 5, prove that**

**Question 1.**

**Solution:**

L.H.S =

(C1 = C3 and C2 = C3)

= 0 + 0

= 0

= R.H.S

**Question 2.**

**Solution:**

L.H.S =

**Question 3.**

**Solution:**

**Question 4.**

**Solution:**

L.H.S =

**Question 5.**

**Solution:**

L.H.S = ∆ =

**By using properties of determinants in Q 6 to 14, show that**

**Question 6.**

**Solution:**

L.H.S = ∆ = …(i)

**Question 7.**

**Solution:**

L.H.S =

**Question 8.**

**(a) **

**(b) **

**Solution:**

(a) L.H.S =

**Question 9.**

**Solution:**

Let ∆ =

Applying R1–>R1 – R2, R2–>R2 – R3

**Question 10.**

**(a) **

**(b) **

**Solution:**

(a) L.H.S =

**Question 11.**

**(a) **

**(b) **

**Solution:**

(a) L.H.S =

=

**Question 12.**

**Solution:**

L.H.S =

**Question 13.**

**Solution:**

L.H.S =

**Question 14.**

**Solution:**

Let ∆ =

This may be expressed as the sum of 8 determinants

**Question 15.**

**If A be a square matrix of order 3×3, then | kA | is equal to**

**(a) k|A|**

**(b) k² |A|**

**(c) k³ |A|**

**(d) 3k|A|**

**Solution:**

Option (c) is correct.

**Question 16.**

**Which of the following is correct:**

**(a) Determinant is a square matrix**

**(b) Determinant is a number associated to a matrix**

**(c) Determinant is a number associated to a square matrix**

**(d) None of these**

**Solution:**

Option (c) is correct

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