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In Exercises $9-16,$ find a basis for the eigenspace corresponding to each listed eigenvalue.$$A=\left[\begin{array}{rr}{7} & {4} \\ {-3} & {-1}\end{array}\right], \lambda=1,5$$

$\lambda=1$ is $\left[\begin{array}{c}{-\frac{2}{3}} \\ {1}\end{array}\right]$$\lambda=5 \mathrm{is}\left[\begin{array}{c}{-2} \\ {1}\end{array}\right]$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 1

Eigenvectors and Eigenvalues

Vectors

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Okay, let's start with Plan B is equal to one. We have a minute. I that's just equal to 64 native, three and negative be writing are augmented matrix We gets 64 general, another three to connect to zero. That reduces to one to over 30000 So our solution, or actually, excellent. It is equal to over to over three x two, and we see that X two is free. So argon space corresponding to Lambda is equal to one is looking to over three and one. Okay, Now let's look at Amanda's equal to five. We get stay minus five. I is equal to 24 negative three. And the Group six. Okay. What is this? Releases? 212 zeroes up. So we can say that our idea of space for landed a good five would be negatives. Two and one

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