Homework #$3$

Using Python, numpy package and linear algebra packages, solve the questions below and print the results on the screen.

$1.$

Find the eigenvalues and eigenvectors of $A=\left[\begin{array}{ccc}2& -1& 0\\ 3& -2& 0\\ 0& 0& 1\end{array}\right].$

Print the results to the screen!

$2.$ Solve the linear systems below $($if a variable is not available, its coefficient is zero!$)$:

a$.$

$x_1-3x_2+4x_3=-4$

$3x_1-7x_2+7x_3=-8$

$-4x_1+6x_2-x_3=7$

b$.$

$x_1-3x_3=8$

$2x_1+2x_2+9x_3=7$

$x_2+5x_3=-2$

c$.$

$x_1-3x_2=5$

$-x_1+x_2+5x_3=2$

$x_2+x_3=0$

Find the inverse of the matrix $A=\left[\begin{array}{ccc}0& 1& 2\\ 1& 0& 3\\ 4& -3& 8\end{array}\right],$ if it exists.

$($First calculate the determinant of the matrix, if it is not zero, then find the inverse$)$