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

### Question 1.

Solution:

The determinant of a 2 x 2 matrix

Hence,

### Question 2. (i)

Solution:

from trigonometric identities

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.

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.

Solution:

### (i)

Solution:

Solving determinants on both sides,

### (ii)

Solution:

Solving determinants on both sides

### (A) 6        (B)  Â±6        (C) -6        (D) 0

Solution:

Solving determinants on both sides

Hence, Option (B)

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