# Class 12 NCERT Solutions – Mathematics Part I – Chapter 4 Determinants – Exercise 4.1

• Last Updated : 04 Mar, 2021

### Question 1. Solution:

The determinant of a 2 x 2 matrix  Hence,  ### Question 2. (i) Solution:  from trigonometric identities

### (ii) Solution:  ### Question 3. If show that Solution:

LHS=>

Matrix, Hence, determinant, RHS=>

Determinant, Now, Hence, proved, LHS = RHS

### Question 4. If then show that | Solution:

LHS=>

Matrix, Hence, determinant, RHS =>

Determinant, Now, Hence, proved, LHS = RHS

### (i) Solution:

Since the maximum number of zeroes are in the second row, we will expand the determinant along row 2. ### (ii) Solution: ### (iii) Solution: Note: This matrix is skew symmetric i.e. For every skew symmetric matrix of “odd dimension”, the determinant vanishes i.e. determinant is zero.

### (iv) Solution:

Since the maximum number of zeroes are in the second row, we will expand the determinant along row 2. ### Question 6. If find |A|

Solution: ### (i) Solution:

Solving determinants on both sides, ### (ii) Solution:

Solving determinants on both sides ### (A) 6        (B)  ±6        (C) -6        (D) 0

Solution:

Solving determinants on both sides Hence, Option (B)

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