Determine the characteristic polynomial of $$.
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The characteristic polynomial of a square matrix $$ is $$.
Let $$.
(a)
Determine the characteristic polynomial of $$.

$$

(b)
What are the real eigenvalues of $$?

List from smallest to largest: $$, $$

Let $$.
(a)
Determine the characteristic polynomial of $$.
-6 $$ $$ $$
(b)
What are the real eigenvalues of $$?

List from smallest to largest: $$, $$, $$

If $$ is triangular, then so is $$ and there is an easy way to determine the determinant of triangular matrices.
Let $$.
(a)
Determine the characteristic polynomial of $$.

$$

(b)
What are the real eigenvalues of $$?

$$

Try cofactor expansion. Also, quadratic formula.
In the characteristic polynomial, $$ what is the multiplicity of$$
(a)
$$? $$
(b)
$$? $$
(c)
$$? $$

True/False: Let $$ be an $$ matrix. $$ is invertible if and only if zero is an eigenvalue of $$.
True False