Class 12 NCERT Solutions- Mathematics Part I – Chapter 4 Determinants – Exercise 4.2 | Set 1
Using the properties of determinants and without expanding in Exercise 1 to 7, prove that:
Question 1.
Solution:
L.H.S.=
C1→C1+C2
=
According to Properties of Determinant
=0 [∵ C1 & C3 are identical]
Now, L.H.S.=R.H.S.
Hence Proved
Question 2.
Solution:
L.H.S.=
=0 [∵ Every element of C1 are 0]
Now, L.H.S.=R.H.S.
Hence Proved
Question 3.
Solution:
L.H.S.=
C3→C3-C1
=
=
=9 ×0=0 [∵C2 & C3 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 Δ=
Taking (-1) common from every row
Δ=(-1)3
Interchange rows and columns
Δ=-
Now, Δ=-Δ
Δ+Δ=0
2Δ=0
Δ=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
By using properties of determinants, in Exercises 8 to 14, show that:
Question 8(i).
(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
Question 10.(i)
(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
Last Updated :
05 Apr, 2021
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