NCERT Solutions Class 12

Exercise 4.1

Evaluate the following determinants in Exercise 1 and 2.

1.  

Ans.   =  =  = 18

---

2. (i) 

(ii)  

Ans. (i)  =  =  = 1

(ii)  = 

=  = 

---

 

3. If A =  then show that  

Ans. Given: A =  then 2A = 

= 

L.H.S. =  = 

R.H.S. = 

=  = 

Since L.H.S. = R.H.S.

Hence, proved.

---

 

4. If A =  then show that  

Ans. Given: A =  then 3A =  = 

L.H.S.   = 

=  = 3 x 36 = 108

R.H.S.   = 

= 27 [1 (4 – 0)] = 27 x 4 = 108

Since   L.H.S. = R.H.S.

Hence, proved.

---

5. Evaluate the determinants:

(i) 

(ii)  

(iii) 

(iv)  

Ans. Evaluate the determinants:

(i) Given: 

Expanding along first row,   

= 

=  = 

(ii) Given: 

Expanding along first row,   

= 

= 

= 21 + 20 + 5 = 46

(iii) Given: 

Expanding along first row,   

= 

= 0 + 6 – 6 = 0

(iv) Given:      

Expanding along first row,   

= 

=  = 5

---

6. If A =  find  

Ans. Given:     A = 

  = 

Expanding along first row,   

= 

= 

= 

=  = 0

---

7. Find the value of  if:

(i) 

(ii) 

Ans. (i) Given: 

 

 

 

 

 

 

(ii) 

 

 

 

---

8. If  then  is equal to:

(A) 6

(B)  

(C)  

(D) 0

Ans. Given: 

 

 

 

 

Therefore, option (B) is correct.