Consider the function f : \mathbb{R}^2 \to \mathbb{R} defined as f(x, y) = x^2y + xy^2 - The tangent plane to the function f at the point (1,1) is given by T_1. Let A_1 denote the affine subspace of \mathbb{R}^3 formed by the set of points on T_1. Let V_1 denote the corresponding vector subspace associated with A_1. - Let A denote the Hessian matrix of the function f at the point (1, 1). - Consider the affine subspace of \mathbb{R}^3 given by A_2 = {(x, y, z) \mid x - y + z = 1, \text{ where } x, y, z \in \mathbb{R}} Let V_2 denote the corresponding vector subspace associated with A_2. Using the above information answer the given subquestions. Which of the following sets forms a basis β of V1?

(B) {(−1, 0,−3), (0, 1, 3)}

Mathematics for Data Science II · End Term · 3 Apr 2022 · January 2022 term

Question 18: Which of the following sets forms a basis β of V1?

Question 18

+3 marksOne correct option

Consider the function $f : \mathbb{R}^2 \to \mathbb{R}$ defined as

$f(x, y) = x^2y + xy^2$
The tangent plane to the function $f$ at the point (1,1) is given by $T_1$ . Let $A_1$ denote the affine subspace of $\mathbb{R}^3$ formed by the set of points on $T_1$ . Let $V_1$ denote the corresponding vector subspace associated with $A_1$ .
Let $A$ denote the Hessian matrix of the function $f$ at the point $(1, 1)$ .
Consider the affine subspace of $\mathbb{R}^3$ given by

$A_2 = \{(x, y, z) \mid x - y + z = 1, \text{ where } x, y, z \in \mathbb{R}\}$

Let $V_2$ denote the corresponding vector subspace associated with $A_2$ .

Using the above information answer the given subquestions.

Which of the following sets forms a basis β of V1?

A
{(1, 0, 1), (0, 1, 1)}
B
{(−1, 0,−3), (0, 1, 3)}
C
{(1, 0,−3), (0, 1, 3)}
D
{(1, 0,−1), (0, 1,−1)}

Show answer

Correct answer

B
{(−1, 0,−3), (0, 1, 3)}

See the whole paper Take it as a mock test

Question 18 of 20 in the IIT Madras BS Mathematics for Data Science II (Maths 2) End Term paper sat on 3 Apr 2022, in the January 2022 term (IIT M FOUNDATION DIPLOMA ENDTERM AN1 3 Apr 2022). It carries 3 marks.

Question 18: Which of the following sets forms a basis β of V1?

Question 18

More questions from this paper