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Questions › CUET-PG › CUET-PG 2023 Shift 2 › Q67
4 marks, −1Mathematics › Vector spaces, rank and eigenvalues › Linear independence, span and basisModerateabout 1 min

CUET-PG 2023 Shift 2 Question 67: Vector spaces, rank and eigenvalues

Find the scalars λ1\lambda_1λ1​ and λ2\lambda_2λ2​ that are attached to v=[12]v = \begin{bmatrix}1\\2\end{bmatrix}v=[12​] and w=[31]w = \begin{bmatrix}3\\1\end{bmatrix}w=[31​] to yield [10]\begin{bmatrix}1\\0\end{bmatrix}[10​]

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Find the scalars λ₁ and λ₂ that are attached to v = [1; 2] and w = [3; 1] to yield [1; 0] (A) λ₁ = 2/5, λ₂ = -2/5 (B) λ₁ = -1/5, λ₂ = 2/5 (C) λ₁ = 5, λ₂ = 1/5 (D) λ₁ = -1/5, λ₂ = -2/5

Also written as: Find the scalars lambda_1 and lambda_2 that are attached to v = [1; 2] and w = [3; 1] to yield [1; 0]

Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.

What this question tests

This question is on Linear independence, span and basis, part of Vector spaces, rank and eigenvalues in Mathematics.

Whether vectors depend on each other, what they span and when they form a basis.

TestStop has 13 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q6Let W be a subspace of a vector space ℝ³. Then which of the following sets of vectors forms a basis of W?
  • IIT JAM 2021 · Q20Let W be the subspace of ℝ³ spanned by (0, -1, 2) and (2, -1, 0). Which one of the following vectors lies in…
Take this paper as a timed mockMore on Linear independence, span and basis

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Question from the CUET-PG 2023 Shift 2 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.