Part BCSIR NET June 2024operator-on-matrices-not-on-vectors

Operator on matrices not on vectors

Let V be the real vector space of 2 × 2 matrices with entries in $R$ . Let T : V → V denote the linear transformation defined by T(B) = AB for all B ∈ V, where A = ((2, 0), (0, 1)). What is the characteristic polynomial of T?

A.(x − 2)(x − 1)
B. $x^{2} (x - 2) (x - 1)$
C. $(x - 2)^{2} (x - 1)^{2}$ ✓
D. $(x^{2} - 2) (x^{2} - 1)$

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: Equivalent matrices are similar

Operator on matrices not on vectors

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