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In Exercises $9-16,$ find a basis for the eigenspace corresponding to each listed eigenvalue.$$A=\left[\begin{array}{ll}{5} & {0} \\ {2} & {1}\end{array}\right], \lambda=1,5$$

Eigen space for eigenvalue $\lambda=1$ is $\left[\begin{array}{l}{0} \\ {1}\end{array}\right]$Eigen space for eigenvalue $\lambda=5$ is $\left[\begin{array}{l}{2} \\ {1}\end{array}\right]$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 1

Eigenvectors and Eigenvalues

Vectors

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allowing once. On this given question, the value off a metrics is 50 to 1. Where to find the value of agony. Space for the Lambda Value one and five. The first of all, for Lambda One, the question is a minor size. It was did you hear? I used Identity Matic identity metrics. So it becomes five minus 1201 minus one. It just request to 5. 34 0 to 0. Documenting metrics will be Jesus! Jesus! Right, So here we can see that. Excellent. It's a quest to judo and x two is free. So the solution can be written in the form off X equals two x two Judo one. Here. This metrics. Jovan, is I gonna space from the definition? Okay. Yeah. Next we'll solve for Lambda is it was 25 So the equation will become a minus five. I is a quest of judo. Hence five minus five, 201 minus five. Which is a cluster judo. Judo do minus four. Next step is to write documented argument and metrics. That is judo 20 minus four. Gino Gino Has this leads to the equation two X one minus four. Next Tuesday it was 20 or X 26. Questo works, too. Yes. The solution can be written in the farm off X equals two x two no one here. This metrics to one is dying in space full for Lambda value of five.

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