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Construct an example of a $2 \times 2$ matrix with only one distinct eigenvalue.

$\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 1

Eigenvectors and Eigenvalues

Vectors

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Okay, So for this particular question, we want to find a two by two matrix with only one distinct the Eden Valley. Well, just said construct an example. Okay, Well, I could construct about two or three examples, but your identity, my tricks, obviously has early one distinct. I value we know that because the characteristic polynomial, we'll just be modest. I land a modest one or square, which is a perfect square. Okay. And obviously the salute when you solve this equal to zero, it has only one solution. So that's one, um, another example. So and then, in fact, that's probably point out if we said this would be I, um other ways lander here, but any multiple of I sew anymore OK, off. I also satisfies this condition too. Okay, Uh, the second example probably ended here. Is any so any back any matrix two by two. Which sort of have the same, um, same Daigle entries. But let's say if I vary it say one and zero. So as long as one of the entries zero one of the off diagonal a treat, this will also sort of fall under the first case here, where the characters, although if also a perfect square, and I'm probably gonna leave it, that because it is pretty simple

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