# NCERT solution class 12 chapter 4 Determinants exercise 4.1 mathematics part 1

## EXERCISE 4.1

#### Question 1:

Evaluate the determinants in Exercises 1 and 2.  = 2(−1) − 4(−5) = − 2 + 20 = 18

#### Question 2:

Evaluate the determinants in Exercises 1 and 2.

(i) (ii) (i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos2 θ+ sin2 θ = 1

(ii) = (x2 − x + 1)(x + 1) − (x − 1)(x + 1)

x3 − x2 + x + x2 − x + 1 − (x2 − 1)

x3 + 1 − x2 + 1

x3 − x2 + 2

#### Question 3:

If , then show that The given matrix is . #### Question 4:

If , then show that The given matrix is .

It can be observed that in the first column, two entries are zero. Thus, we expand along the first column (C1) for easier calculation.  From equations (i) and (ii), we have: Hence, the given result is proved.

#### Question 5:

Evaluate the determinants

(i) (iii) (ii) (iv) (i) Let .

It can be observed that in the second row, two entries are zero. Thus, we expand along the second row for easier calculation. (ii) Let .

By expanding along the first row, we have: (iii) Let By expanding along the first row, we have: (iv) Let By expanding along the first column, we have: #### Question 6:

If , find .

Let By expanding along the first row, we have: #### Question 7:

Find values of x, if

(i)

2451=2x46x(ii)

2345=x32x5

(i)  (ii)  #### Question 8:

If , then x is equal to

(A) 6 (B) ±6 (C) −6 (D) 0   