Let P = 
, where α ∈ R. Suppose Q = [q ij ] is a matrix such that PQ = k Ι , where k ∈ R, k ≠ 0 and Ι is the identity matrix of order 3. If q 23 = – 
and det (Q) = 
, then
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b,c)
Sol. As PQ = k Ι ⇒ Q = kP –1 Ι
now Q = 
(adjP) Ι ⇒ Q = 
q 23 = 
⇒ 
(–3 α – 4) = 
⇒ 2(3 α + 4) = 5 + 3 α
3 α = – 3 ⇒ α = –1
also |Q| = 
⇒ 
(20 + 12 α ) = 2k ⇒ 8 = 2k ⇒ k = 4
incorrect
correct
|P(adjQ)| = |P| |adjQ| = P| |Q| 2 = 2 2 (2 3 ) 2 = 2 9 correct
|Q(adjP)| = |Q| |adjP| = |Q| |P| 2 = 2 3 (2 3 ) 2 = 2 9 incorrect
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