Skip to content
Part CCSIR NET June 2024free-coordinate-from-a-basis-vector

Free coordinate from a basis vector

Let V be the subspace spanned by the vectors v1=(1,0,2,3,1),v2=(0,0,1,3,5),v3=(0,0,0,0,1)v_{1} = (1, 0, 2, 3, 1), v_{2} = (0, 0, 1, 3, 5), v_{3} = (0, 0, 0, 0, 1) in the real vector space R5\mathbb{R}^{5}. Which of the following vectors are in V?

  1. A.(1, 1, 1, 1, 1)
  2. B.(0, 0, 1, 2, 4)
  3. C.(1, 0, 1, 0, 1)✓ Correct
  4. D.(1, 0, 1, 0, 2)✓ Correct

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: An injective linear operator on a vector space is surjective

More on this topic

The chapter behind this: Bases, dimension and rank — free to read

From Vector Spaces and Linear Maps › Bases, dimension, rank–nullity

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram