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Question: If A =\(\begin{bmatrix} 2 & –1 \\ –1 & 2 \end{bmatrix}\) and A<sup>2</sup> – 4A – n I = 0, then n is...

If A =[2–1–12]\begin{bmatrix} 2 & –1 \\ –1 & 2 \end{bmatrix} and A2 – 4A – n I = 0, then n is equal to

A

13\frac{1}{3}

B

–13–\frac{1}{3}

C

– 3

D

3

Answer

– 3

Explanation

Solution

∣2–λ–1–12–λ∣\left| \begin{matrix} 2–\lambda & –1 \\ –1 & 2–\lambda \end{matrix} \right| = 0

4 + l2 – 4l – 1 = 0

l2 – 4l + 3 = 0

A2 – 4A + 3I = 0

–n = 3 & n = – 3