Part CCSIR NET December 2024the-two-matrices-represent-one-map-so-t-is-similar-to-t-squared

The two matrices represent one map so t is similar to t squared

Let $T : C^{2} \to C^{2}$ be $a C -$ linear transformation. For any ordered basis ℬ of $C^{2}$ , let [T]ℬ denote the matrix of T with respect to ℬ. Suppose that ℬ $_{1}$ and ℬ $_{2}$ are two ordered bases of $C^{2}$ such that the matrix [T](ℬ $_{1})$ is upper-triangular and [T]_(ℬ $_{2}) = ([T]_{(}$ ℬ $_{1}))^{2}$ . Which of the following statements are FALSE?

A.The characteristic polynomial of T can be $x^{2} + x + 1$ .
B.The characteristic polynomial of T can be x(x − 1).
C.The minimal polynomial of T can be $x^{2}$ .✓
D.The characteristic polynomial of T can be $x (x - e^{(} 2 π i /3))$ .✓

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.

See pricing

50 are analysed free — try those first.

Related counterexample: Same characteristic polynomial ⇒ similar

The two matrices represent one map so t is similar to t squared

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