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Part BCSIR NET June 2024one-eigenvalue-is-one-equation

One eigenvalue is one equation

Let ((2, a), (b, c)) be a 2 × 2 real matrix for which 6 is an eigenvalue. Which of the following statements is necessarily true?

  1. A.24 − ab = 4c✓
  2. B.a + b = 8
  3. C.c = 6
  4. D.ab = 0

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.

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50 are analysed free — try those first.

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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