# 1-Find the characteristic polynomial of Ax 2 -2 -2A= ( 0 -5 -6 ) 0 8 9

. Use for the variable in the polynomial.

2-List all of the distinct eigenvalues of *A*. Enter your answer as a list of numbers separated by commas.

7 0 -2

A= ( 15 0 -6 )

15 0 -4

3-Find all distinct eigenvalues of *A*. Then find the basic eigenvectors of *A* corresponding to each eigenvalue.

For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue

0 -6 0

A= ( 0 -2 0 )

1 -6 -1

4-Find an invertible matrix *P* and a diagonal matrix *D* such that *P*^{−1}*AP*=*D*.

3 0 0

A= ( -20 3 10 )

10 0 -2

5-Find the point 1/4 of the way from (10, 9, 4) to (7, 7, −2).

6-Find the vector equation for the line passing through the points *P*_{1}(−1, 6, 8) and *P*_{2}(−7, 12, 18).

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