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In Exercises $7-12$ , use Example 6 to list the eigenvalues of $A$ . In each case, the transformation $\mathbf{x} \mapsto A \mathbf{x}$ is the composition of a rotation and a scaling. Give the angle $\varphi$ of the rotation, where $-\pi<\varphi \leq \pi,$ and give the scale factor $r .$$$\left[\begin{array}{rr}{-5} & {-5} \\ {5} & {-5}\end{array}\right]$$

$A = \left[ \begin{array} { c c } { - 5 } & { - 5 } \\ { 5 } & { - 5 } \end{array} \right]$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 5

Complex Eigenvalues

Vectors

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so for probably 10. Well, given the Matrix that ISS next 55 life and make define, so can we need to apply our result in exactly six. So here we take Hey, I hate to be dignified, maybe five now so number will be making five minus five I and to scale The interpretation is fine hour, which is well, I was queer Time Fast five squared Take a square root so this will be by Times Square two. So see, we'll be five times going to times the matrix well active, one over. Scared, too. So it's just out right down as a screw to over two negative square to two. It's 3 to 2, and negatives were to to, so we can take to be negative. So just posted Ri Pi over four so that our matrix will be five squared over square two times. No sign, it's reply or by this sign, reply or sighing, reply over four and co sign reply or four

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If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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