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GATE 2020 ME (ME2) – Question 29

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

Let I be the 100-dimensional identity matrix, and E the set of its distinct real eigenvalues (no value repeated). Find the number of elements in E.

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Correct answer: 1 to 1

Explanation

Every nonzero vector satisfies Iv=v, so its eigenvalue is1. Although this eigenvalue has algebraic multiplicity100, the set of distinct values is just{1}. **Answer:1**.