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Part CCSIR NET June 2025matching-characteristic-polynomials-settles-nothing-compute-the-nullities

Matching characteristic polynomials settles nothing compute the nullities

Which of the following matrices are similar over to the matrix A whose rows are (−1, 1, 0, 0), (0, −1, 0, 0), (0, 0, 1, 1) and (0, 0, 0, 1)?

  1. A.The matrix with rows (0, 0, 0, −1), (1, 0, 0, 0), (0, 1, 0, 2), (0, 0, 1, 0)✓
  2. B.The matrix with rows (0, 0, 0, 1), (1, 0, 0, 0), (0, 1, 0, −2), (0, 0, 1, 0)
  3. C.The matrix with rows (0, 1, 1, 0), (1, 0, 0, 1), (0, 0, 0, 1), (0, 0, 1, 0)✓
  4. D.The matrix with rows (0, 1, 0, 0), (1, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 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, and why this one tests invariants don't determine.

See pricing

50 are analysed free — try those first.

The trap it tests

Invariants don't determine

Two objects sharing an invariant were treated as the same object.

Drill statements like this

Related counterexample: Every real matrix has a Jordan form over ℝ

More on this topic

The chapter behind this: Jordan canonical form — free to read

From Eigenvalues and Canonical Forms › Jordan canonical form

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