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GATE 2019 ME (ME1) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

For $$P=\begin{bmatrix}1&1&0\\0&1&1\\0&0&1\end{bmatrix},$$ find the number of distinct eigenvalues.

  1. 0
  2. 1
  3. 2
  4. 3

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Correct answer: (B) 1

Explanation

P is upper triangular, so its eigenvalues are its diagonal entries: 1,1,1. The characteristic polynomial is $(1-\lambda)^3$. Although the eigenvalue has algebraic multiplicity three, there is only **one distinct eigenvalue, B**.