VectorHard

Question

If and are linearly dependent vectors and , then

Options

A.α = 1, β = - 1
B.α = 1, β = 1
C.α = - 1, β = 1
D.α = 1, β = 1

Solution

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

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