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AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper
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© examsnet.com
Question : 4
Total: 160
If A =
[
p
q
r
r
p
q
q
r
p
]
and
A
A
T
= I then ,
p
3
+
q
3
+
r
3
=
± 1
pqr
3 pqr
3 pqr ± 1
Validate
Solution:
It is given that,
A
A
T
=
I
It is an orthogonal matrix and the determinant of orthogonal
matrix is ±1
|
p
q
r
r
p
q
q
r
p
|
=
±
1
Solve the above determinant,
p
3
−
p
q
r
−
p
q
r
+
q
3
+
r
3
=
±
1
p
3
+
q
3
+
r
3
−
3
p
q
r
=
±
1
p
3
+
q
3
+
r
3
=
3
p
q
r
±
1
© examsnet.com
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