IITM BS Question 16 - Week 10 Practice

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IITM BS Question 16 - Week 10 Practice | Prasnya

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Q16Comprehension2 Marks31 Aug 2025

Passage

Based on the above data, answer the given subquestions. Let

f: \mathbb{R}^2 \to \mathbb{R}

be the real-valued function defined by

f(x, y) = x^2 - xy + y^2

, for all

(x, y) \in \mathbb{R}^2

. Let

T(3, 1)

denote the tangent plane to the graph of

f

at the point

(3, 1)

. Since

T(3, 1)

is an affine subspace of

\mathbb{R}^3

, there exists a vector

v \in \mathbb{R}^3

and a unique subspace

U \subset \mathbb{R}^3

such that

T(3, 1) = v + U = \{ v + u \mid u \in U \}

Which of the following is a basis for U?

Q16

00:00

31 Aug 2025

Mathematics 2 · Week 10

Q16.Which of the following is a basis for U?@passage

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