Mathematics · Integral Equations
Let K(x, y) be a kernel on [0, 1] × [0, 1] defined by K(x, y) = sin(2πx)sin(2πy). Consider the linear integral operator T defined on the space of continuous functions C([0, 1]) by: (Tu)(x) = ∫01 u(y)K(x, y)dy Which of the following assertions is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1The null space of T is finite-dimensional
- 2∫01 v(x)(Tu)(x)dx = ∫01 (Tv)(x)u(x)dx for all u, v ∈ C([0, 1])✓
- 3T has at least one negative eigenvalue
- 4T has an eigenvalue strictly greater than 3/4
Correct answer
∫01 v(x)(Tu)(x)dx = ∫01 (Tv)(x)u(x)dx for all u, v ∈ C([0, 1])
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Integral Equations MCQs →Want more practice questions on Integral Equations?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Integral Equations