TS EAMCET 20-July-2022 Shift 2 Solved Paper

Given A=[

a	b	c
d	e	f
g	h	i

]
∵ Given that A is a skew-symmetric matrix.
‌AT=−A
⇒[

a	d	g
b	e	h
c	f	i

]=−[

a	b	c
d	e	f
g	h	i

]
⇒[

a	d	g
b	e	h
c	f	i

]=[

−a	−b	−c
−d	−e	−f
−g	−h	−i

]
On comparing corresponding elements, we get
a‌=−a
⇒‌‌2a‌=0⇒a=0
e‌=−e⇒2e=0⇒e=0
i‌=−i⇒2i=0⇒i=0
Now,
‌d=−b....(i)
‌g=−c....(ii)
‌b=−d....(iii)
‌h=−f....(iv)
‌c=−g....(v)
‌f=−h....(vi)
Eq. (iii) divide by Eq. (v),
‌

b

c

=‌

−d

−g

⇒‌‌‌

b

c

=‌

−d

g

×(−1) ...(vii) Eq. (iii)
Eq. (iv) gives ‌

h

f

=−1 and Eq. (vi) gives ‌

f

h

=−1
But for h=0,‌

f

h

is not defined.
On putting (−1)=‌

h

f

in Eq. (viii),
‌

b

c

=‌

−d

g

×‌

h

f

=‌

−dh

gf

On putting (−1)=‌

h

f

in Eq. (viii),
‌

b

c

=‌

−d

g

×‌

h

f

=‌

−dh

gf