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Part BCSIR NET June 2025trace-of-a-squared-is-not-the-determinant-square-the-sum-first

Trace of a squared is not the determinant square the sum first

Which of the following polynomials is the characteristic polynomial of a real 2 × 2 matrix A such that trace(A) = 7 and trace(A2)=29(A^{2}) = 29?

  1. A.t2+7t+10t^{2} + 7t + 10
  2. B.t2−7t+29t^{2} - 7t + 29
  3. C.t2−7t−10t^{2} - 7t - 10
  4. D.t2−7t+10t^{2} - 7t + 10✓ Correct

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

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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