# Class 12 NCERT Solutions- Mathematics Part I – Chapter 4 Determinants – Exercise 4.2 | Set 1

### Question 1.

Solution:

L.H.S.=

C1â†’C1+C2

=

According to Properties of Determinant

=0                                [âˆµ  C1 & C3 are identical]

Now, L.H.S.=R.H.S.

Hence Proved

### Question 2.

Solution:

L.H.S.=

=0                        [âˆµ Every element of C1 are 0]

Now,  L.H.S.=R.H.S.

Hence Proved

### Question 3.

Solution:

L.H.S.=

C3â†’C3-C

=

=

=9 Ã—0=0          [âˆµC2 & C are identical]

Now,  L.H.S.=R.H.S.

Hence Proved

### Question 4.

Solution:

L.H.S.=

=

Now,  L.H.S.=R.H.S.

Hence Proved

### Question 5.

Solution:

L.H.S.=

Now, L.H.S.=R.H.S.

Hence Proved

### Question 6.

Solution:

Let Î”=

Taking (-1) common from every row

Î”=(-1)3

Interchange rows and columns

Î”=-

Now, Î”=-Î”

Î”+Î”=0

2Î”=0

Î”=0

Now,  L.H.S.=R.H.S.

Hence Proved

### Question 7.

Solution:

L.H.S.=

Taking common a from Row 1,

b from Row 2,

c from Row 3, we have

Now,  L.H.S.=R.H.S.

Hence Proved

### (ii)

Solution:

(i) L.H.S.=

Now,  L.H.S.=R.H.S.

Hence Proved

(ii)  L.H.S.=

Now,  L.H.S.=R.H.S.

Hence Proved

### Question 9.

Solution:

L.H.S.=

Now, L.H.S.=R.H.S.

Hence Proved

### (ii)

Solution:

(i) L.H.S.=

Now,  L.H.S.=R.H.S.

Hence Proved

(ii) L.H.S.=

Now,  L.H.S.=R.H.S.

Hence Proved

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