Skip to main content
MathidiaMathematics Academy
Eigenvalues and diagonalisation
Lesson 6 of 10
Standard practice

Finding eigenvectors

Objective. Find an eigenvector for a known eigenvalue.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Solve (A − λI)v = 0. The solution set is a subspace, so any non-zero multiple of the vector you find is also an eigenvector.

Worked example

For A = [[2, 1], [1, 2]] and λ = 3, find an eigenvector.

For A = [[2
Illustrated card showing For A = [[2
  1. 1A − 3I = [[−1, 1], [1, −1]].
  2. 2The equation gives −x + y = 0, so y = x.
  3. 3Take x = 1.

Answer: (1, 1) or any non-zero multiple

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Reporting the zero vector as the solution of (A − λI)v = 0.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard