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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 351
Question 351 of 472
Medium
MCQ
Let A = \[\left( {
(
0
2
q
r
p
q
−
r
p
−
q
r
)
\begin{pmatrix} 0 & {2q} & r \\ p & q & { - r} \\ p & { - q} & r \\ \end{pmatrix}
0
p
p
2
q
q
−
q
r
−
r
r
} \right).\] If AAT = I3, then \[\left| p \right|\] is :
A
\[{1 \over {\sqrt 2 }}\]
B
\[{1 \over {\sqrt 5 }}\]
C
\[{1 \over {\sqrt 6 }}\]
D
\[{1 \over {\sqrt 3 }}\]
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Official solution
A is orthogonal matrix \[ \Rightarrow \] 02 + p2 + p2 = 1 \[ \Rightarrow \] \[\left| p \right| = {1 \over {\sqrt 2 }}\]
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