VectorHard
Question
If 
and 
are linearly dependent vectors and 
, then
and are linearly dependent vectors and , thenOptions
A.α = 1, β = - 1
B.α = 1, β = 
1
1C.α = - 1, β = 1
1D.α = 1, β = 1
1, β = 1Solution
Since, 
are linearly dependent vectors.
⇒
⇒
= 0
Applying C2 → C2 - C1, C3 → C3 - C
⇒
= 0
⇒ -(β - 1) = 0 ⇒ β = 1
Also,
(given)
⇒ 1 + α2 + β2 = 3 (given
)
⇒ 1 + α2 + 1 = 3
⇒ α2 = 1 ⇒ α =1
are linearly dependent vectors.⇒
⇒
= 0 Applying C2 → C2 - C1, C3 → C3 - C
⇒
= 0⇒ -(β - 1) = 0 ⇒ β = 1
Also,
(given) ⇒ 1 + α2 + β2 = 3 (given
)⇒ 1 + α2 + 1 = 3
⇒ α2 = 1 ⇒ α =
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