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Part BCSIR NET June 2025constant-row-sums-give-both-the-eigenvector-and-the-bound

Constant row sums give both the eigenvector and the bound

Consider the real matrix A whose rows are (29, 0, 55, 17), (1, 28, 46, 26), (17, 13, 33, 38) and (21, 67, 0, 13). What is the largest real eigenvalue of A?

  1. A.101✓
  2. B.67
  3. C.103
  4. D.113

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests standard counterexample.

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50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

Related counterexample: Same characteristic polynomial ⇒ similar

More on this topic

The chapter behind this: Characteristic vs minimal polynomial — what each tells you — free to read

From Eigenvalues and Canonical Forms › Eigenvalues, characteristic & minimal polynomials, Cayley–Hamilton

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