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Exercises $9-14$ require techniques from Section $3.1 .$ Find the characteristic polynomial of each matrix, using either a cofactor expansion or the special formula for $3 \times 3$ determinants described prior to Exercises $15-18$ in Section $3.1 .$ INote: Finding the characteristic polynomial of a $3 \times 3$ matrix is not easy to do with just row operations, because the variable $\lambda$ is involved.$$\left[\begin{array}{rrr}{5} & {-2} & {3} \\ {0} & {1} & {0} \\ {6} & {7} & {-2}\end{array}\right]$$

$-\lambda^{3}+4 \lambda^{2}+25 \lambda-28$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 2

The Characteristic Equation

Vectors

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Okay, So what is lost? A minus lamb that I gives me five minus lambda. Negative too. 301 Minus lambda 067 and negative to minus two. Or mine if Lambda. Now, let's take the determinant of this. What do we get? Ah, for yet five. My is Lambda one minus lambda in two minutes. Linda Minus 18 times one minus Lambda, which simplifies to negative from the Cube post war. And I am the squared. I was 25 pounds, minus 10 8

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