- #1
Mathman23
- 254
- 0
Hi
I have this here matrix
[tex]A = \left[ \begin{array}{ccc} 2 & 1 & 0 \\ 0 & 1 & 0 \\ 3 & 3 & 0 \end{array} \right][/tex]
I calculate the eigenvalues and get (2,1,-1)
Next I calculate the eigenvectors and get (1,0,1) and (-1,1,0) and (0,0,0)
My professor says my third eigenvector is wrong and it should (0,0,1)
My calculation:
[tex]A = \left[ \begin{array}{ccc} (2-(-1) & 1 & 0 \\ 0 & (1-(-1) & 0 \\ 3 & 3 & 1-(-1) \end{array} \right]
= \left[ \begin{array}{ccc} 3 & 1 & 0 \\ 0 & 2 & 0 \\ 3 & 3 & 0 \end{array} \right][/tex]
Then according to the theorem regarding eigenvectors:
[tex]\left[ \begin{array}{ccc} 3 & 1 & 0 \\ 0 & 2 & 0 \\ 3 & 3 & 0 \end{array} \right] \left[ \begin{array}{c} v_1 \\ v_2 \\ v_3 \end{array} \right] = \left[ \begin{array}{c} 0 \\ 0 \\ 0 \end{array} \right] [/tex]
then
[tex]3v_1 + v_2 = 0[/tex]
[tex] 2v_2 = 0[/tex]
[tex]3v_1 + 3 v_2 = 0[/tex]
Is my calculations correct ??
sincerley and best regards,
Fred
I have this here matrix
[tex]A = \left[ \begin{array}{ccc} 2 & 1 & 0 \\ 0 & 1 & 0 \\ 3 & 3 & 0 \end{array} \right][/tex]
I calculate the eigenvalues and get (2,1,-1)
Next I calculate the eigenvectors and get (1,0,1) and (-1,1,0) and (0,0,0)
My professor says my third eigenvector is wrong and it should (0,0,1)
My calculation:
[tex]A = \left[ \begin{array}{ccc} (2-(-1) & 1 & 0 \\ 0 & (1-(-1) & 0 \\ 3 & 3 & 1-(-1) \end{array} \right]
= \left[ \begin{array}{ccc} 3 & 1 & 0 \\ 0 & 2 & 0 \\ 3 & 3 & 0 \end{array} \right][/tex]
Then according to the theorem regarding eigenvectors:
[tex]\left[ \begin{array}{ccc} 3 & 1 & 0 \\ 0 & 2 & 0 \\ 3 & 3 & 0 \end{array} \right] \left[ \begin{array}{c} v_1 \\ v_2 \\ v_3 \end{array} \right] = \left[ \begin{array}{c} 0 \\ 0 \\ 0 \end{array} \right] [/tex]
then
[tex]3v_1 + v_2 = 0[/tex]
[tex] 2v_2 = 0[/tex]
[tex]3v_1 + 3 v_2 = 0[/tex]
Is my calculations correct ??
sincerley and best regards,
Fred