M.Tech Advanced Mathematics Question Bank

Play an AI-generated podcast conversation about this lesson

What are the salient features of the M.Tech (Maths) E-notes?

Fully computerised notes 2. Unit-wise and topic wise important solved problems 3. Practice problems with answers 4. Some important solved previous year's questions 5. Some important video lectures

When do the new batches for M.Tech (Advanced Mathematics) start?

8th January 2023

What is the cost of the M.Tech (Maths) E-notes?

3500

What is the solution available for RGPV papers?

500/- per semester (only Maths) Signup and view all the answers

What is the differential equation that defines the set W of solutions y = f(x)?

2 d^2y/dx^2 - 9 dy/dx + 2y = 0 Signup and view all the answers

Show that W = { (a1, a2, a3) : a1, a2, a3 ∈ F and a1 + a2 + a3 = 0 } is a subspace of V3(F).

To show that W is a subspace of V3(F), we need to demonstrate that it is closed under addition and scalar multiplication, and that it contains the zero vector. Signup and view all the answers

Prove that the set W = {(x, 2x, -3x, x)} is a sub-space of V4(F).

To prove that W is a sub-space of V4(F), we need to show that it satisfies the three conditions for a sub-space: closure under addition, closure under scalar multiplication, and contains the zero vector. Signup and view all the answers

Show that the set W = {(a, b, c) : a - 3b + 4c = 0, for all a, b, c ∈ R} is a sub-space of the 3-tuples vector space V3(R).

In order to prove that W is a sub-space of V3(R), we need to demonstrate that it satisfies the three conditions for a sub-space: closure under addition, closure under scalar multiplication, and contains the zero vector. Signup and view all the answers

Find whether the set of vectors v1 = (1, 2, 1), v2 = (3, 1, 5) and v3 = (3, -4, 7) is linearly independent or dependent.

The set of vectors is linearly independent if the only solution to the equation c1v1 + c2v2 + c3v3 = 0 is c1 = c2 = c3 = 0. Otherwise, the set is linearly dependent. Signup and view all the answers

Prove that the vectors α1 = (1, 2, 3), α2 = (1, 0, 0), α3 = (0, 1, 0), and α4 = (0, 0, 1) in V3(R) form a linearly dependent set.

To prove that the vectors form a linearly dependent set, we need to show that there exist constants c1, c2, c3, and c4, not all zero, such that c1α1 + c2α2 + c3α3 + c4α4 = 0. Signup and view all the answers

Prove that the vectors α1 = (1, 0, -1), α2 = (1, 2, 1), and α3 = (0, -3, 2) form a basis of V3(R).

To prove that the vectors form a basis, we need to show that they are linearly independent and span V3(R). Signup and view all the answers

Show that the vectors (1, 0, 0), (1, 1, 0), and (1, 1, 1) form a basis for R3.

To show that the vectors form a basis, we need to demonstrate that they are linearly independent and span R3. Signup and view all the answers

Show that the vectors (2, 1, 4), (1, -1, 2), and (3, 1, -2) form a basis for R3.

To show that the vectors form a basis, we need to demonstrate that they are linearly independent and span R3. Signup and view all the answers

Prove that the mapping T: V3(R) → V3(R), defined as T(x1, x2, x3) = (x1 - x2 + x3, -x2), for all x1, x2, x3 ∈ R, is a linear transformation.

To prove that T is a linear transformation, we need to show that it satisfies the two conditions: T(u + v) = T(u) + T(v) and T(kv) = kT(v). Signup and view all the answers

Prove that the mapping T: R2 → R3, defined by T(a, b) = (a - b, b - a, -a), for all a, b ∈ R, is a linear transformation.

To prove that T is a linear transformation, we need to show that it satisfies the two conditions: T(u + v) = T(u) + T(v) and T(kv) = kT(v). Signup and view all the answers

Find the value of H0(x), H1(x), H2(x), H3(x), and H4(x).

The values of H0(x), H1(x), H2(x), H3(x), and H4(x) can be found using the recurrence relation and formulas for Hermite polynomials. Signup and view all the answers

M.Tech Advanced Mathematics Question Bank

Choose a study mode

Podcast

Questions and Answers