## Hello Students! In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 4.3**.

You can download the **PDF of NCERT Books Maths Chapter 4** for your easy reference while studying **NCERT Solutions for Maths Class 12 Exercise 4.3**.

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**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 4.4**

**NCERT Solutions for Maths Class 12 Exercise 4.5**

**NCERT Solutions for Maths Class 12 Exercise 4.3**

**Maths Class 12 Ex 4.3 Question 1.**

**Write the Minors and Cofactors of the elements of following determinants:**

**Solution:**

**Solution:**

**(i)** Let A =

M_{11} = Minor of a_{11} = 3, M_{12} = Minor of a_{12 }= 0,

M_{21} = Minor of a_{21 }= –4, M_{22 }= Minor of a_{22 }= 2

Now, cofactors of a_{ij} is A_{ij}.

So, A_{11} = (–1)^{1 + 1} M_{11} = (–1)^{2} (3) = 3

A_{12} = (–1)^{1 + 2} M_{12} = (–1)^{3} (0) = 0

A_{21} = (–1)^{2 + 1} M_{21} = (–1)^{3} (–4) = 4

A_{22} = (–1)^{2 + 2} M_{22} = (–1)^{4} (2) = 2

**(ii)** Let A =

M_{11} = Minor of a_{11} = d, M_{12} = Minor of a_{12 }= b,

M_{21} = Minor of a_{21 }= c, M_{22 }= Minor of a_{22 }= a

Now, cofactors of a_{ij} is A_{ij}.

So, A_{11} = (–1)^{1 + 1} M_{11} = (–1)^{2} (d) = d

A_{12} = (–1)^{1 + 2} M_{12} = (–1)^{3} (b) = –b

A_{21} = (–1)^{2 + 1} M_{21} = (–1)^{3} (c) = –c

A_{22} = (–1)^{2 + 2} M_{22} = (–1)^{4} (a) = a

**Maths Class 12 Ex 4.3 Question 2.**

**Write Minors and Cofactors of the elements of following determinants:**

**Maths Class 12 Ex 4.3 Question 3.**

**Using Cofactors of elements of second row, evaluate**

**Solution:**

The elements of second row are 2, 0 and 1.

**Maths Class 12 Ex 4.3 Question 4.**

**Using Cofactors of elements of third column, evaluate**

**Solution:**

**Solution:**

The elements of third column are yz, zx and xy.

**Maths Class 12 Ex 4.3 Question 5.**

**If **** and A**_{ij} is Cofactors of a_{ij}, then value of ∆ is given by

**(A) a**_{11 }A_{31 }+ a_{12 }A_{32 }+ a_{13 }A_{33}

**(B) a**_{11 }A_{11 }+ a_{12 }A_{21 }+ a_{13 }A_{31}

**(C) a**_{21 }A_{11 }+ a_{22 }A_{12 }+ a_{23 }A_{13}

**(D) a**_{11 }A_{11 }+ a_{21 }A_{21 }+ a_{31 }A_{31}

_{ij}is Cofactors of a

_{ij}, then value of ∆ is given by

_{11 }A

_{31 }+ a

_{12 }A

_{32 }+ a

_{13 }A

_{33}

_{11 }A

_{11 }+ a

_{12 }A

_{21 }+ a

_{13 }A

_{31}

_{21 }A

_{11 }+ a

_{22 }A

_{12 }+ a

_{23 }A

_{13}

_{11 }A

_{11 }+ a

_{21 }A

_{21 }+ a

_{31 }A

_{31}

**Solution:**

Option (D) is correct.

Related Links:

**NCERT Solutions for Maths Class 12 Exercise 4.1**

**NCERT Solutions for Maths Class 12 Exercise 4.2**