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MMLU / Suppose A is a 3 × 3 matrix such that det(A − λI) = −λ^3 + 3λ^2 + λ − 3, where I…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose A is a 3 × 3 matrix such that det(A − λI) = −λ^3 + 3λ^2 + λ − 3, where I is the 3 × 3 identity matrix. Which of the following are TRUE of A?
I. The trace of A is 3.
II. The determinate of A is −3.
III. The matrix A has eigenvalues −3 and 1.

choices

  1. I only
  2. II only
  3. III only
  4. I and II only

subject

college_mathematics

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Source and history

task_id
2c78f0aa-d09c-526c-a980-4f8520031ec8
task_key
all--test--2c78f0aa-d09c-526c-a980-4f8520031ec8
task_revision_id
1
config / split
all / test

Official source

initial import