Exercise 4.1

Download as PDF

NCERT Solutions class 12 Maths Determinants

Evaluate the following determinants in Exercise 1 and 2.

1.  

Ans.   =  =  = 18

2. (i)

(ii)  

Ans. (i) =  =  = 1

(ii) =

=  =

NCERT Solutions class 12 Maths Exercise 4.1

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.

NCERT Solutions class 12 Maths Exercise 4.1

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.