# EXERCISE 4.1 ( Determinants )

Evaluate the determinant:(Class 12 ncert solution math exercise 4.1)

Question 1:

Solution: Let

Hence,

Question 2: Evaluate the determinants:

(i)

(ii)

Solution: (i)

(ii)

Question 3: If , then show that

Solution: The given matrix is

Therefore,

Hence,

Now,

Therefore,

Thus, proved.

Question 4: If , then show that

Solution:The given matrix is

It can be observed that in the first column, two entries are zero. Thus, we expand along the first column for easier calculation.

Therefore,

Now,

Therefore,

From equations and ,

Thus, proved.

Question 5:Evaluate the determinants

(i)

(ii)

(iii)

(iv)

Solution:

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

Hence,

(ii) Let

Hence,

(iii) Let

Hence,

(iv)

Hence,

Question 6:If , find

Solution: Let

Hence,

Question 7: Find the values of , if
(i)
(ii)

Solution: (i)

Therefore,

(ii)

Therefore,

Question 8: If , the is equal to
(A) 6
(B)
(C)
(D) 0

Solution:

Therefore,

Thus, the correct option is B.