The value of non-zero scalars α and β for all vectors and , such that is:

Question

Question

This question was previously asked in

NIMCET 2019 Official Paper

Answer 1

Concept:

If two vectors and are equal, then a1 = b1, a2 = b2 and c1 = c2.

Calculation:

It is given that .

⇒

Comparing the scalar coefficients on both sides, we get:

2α + β = -1 ... (1)

-α + 2β = 8 ... (2)

Adding twice the equation (2) with the equation (1), we get:

5β = 15

⇒ β = 3

And using either equation (1) or (2), we get:

α = -2

Hence, α = -2, β = 3.