ex 1.3 Ex. 1.3. For the following 3 x 3 matrices find their characteristic equations, their eigenvalues and the corresp...

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Ex. 1.3. For the following 3 x 3 matrices find their characteristic equations, their eigenvalues and the corresponding eigenv

ex 1.3

Answer 1

Answer #1

ex1.3)b)

$The eigenvalues of Aare the roots of the characteristic equation det (A AI) = 0 E(E)-G)-E3) 1 0 0 5 - A 1 1 det - 0 1 0 0 0 1$

$-13 122-3928$ is characteristic equation.

$-312 39 28 0 - (A 1) (A 4) ( 7) 0 A1,4,7$

$Eigenvectors for A= 1 1 0-1 0 1 2 0 0 0 -6E 9-0E:9-0 (A 11)y y z0 ly 2z 0 -2 1$

$Eigenvectors for A=4 (1 0 1 0 1- 0 0 0 -6E (A 41)y 0 y Jx -0 ly-0 60 1$

$Eigenvectors for A 7 0-C 1 0 0 1 1 (A 7I)y y 0 0 0/ Sy=0 GD 0 1$

$The eigenvectors are -1\ 1 -2 1 1$

Answer 2

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