Mathematics · Linear Algebra

Let V (≠ {0}) be a finite-dimensional vector space over ℝ and T: V → V be a linear operator. Suppose that the kernel of T equals the image of T. Which of the following statements is necessarily true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

The dimension of V is even

Save this question and verified answer as a clean study sheet with live clickable link.

👥

Challenge your peer aspirants on WhatsApp or Telegram to solve this question!

Online Test Series

Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.

Chapter Practice

Want more practice questions on Linear Algebra?

Solve complete topic-wise tests with detailed solutions on GkGet.

Recommended practice questions in Mathematics · Linear Algebra

The Dandi March, also known as the Salt Satyagraha, was led by which influential leader?

Which act formally granted independence to India, marking the end of British rule?

Who was the key figure in establishing the Indian National Congress?

Let V (&ne; {0}) be a finite-dimensional vector space over ℝ and T: V &rarr; V be a linear operator. Suppose that the kernel of T equals the image of T. Which of the following statements is necessarily true?