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Geometric Multiplicity need help

  • Thread starter chuy52506
  • Start date
  • #1
77
0

Homework Statement


[tex]\lambda[/tex]=0 is an eigenvalue of
A=
|1 1 1 1 1|
|1 1 1 1 1|
|1 1 1 1 1|
|1 1 1 1 1|
|1 1 1 1 1|

Homework Equations


Find the geometric multiplicity of [tex]\lambda[/tex]=0 as an eigenvalue of A


The Attempt at a Solution


I row reduced it then got the last four rows of all 0s but dont know where to go from there??
 

Answers and Replies

  • #2
77
0
now i have x1=-x2-x3-x4-x5
does that mean it has geom mult of 5?
 
  • #3
360
0
Now you have 4 free variables, namely [itex]x_2, x_3, x_4, x_5 [/itex]. If that doesn't tell you right away, set [itex]x_2 = t_1 [/itex], [itex]x_3 = t_2 [/itex], etc. This gives you
[tex]
\begin{pmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4 \\
x_5
\end{pmatrix}=
\begin{pmatrix}
-t_1 - t_2 - t_3 - t_4 \\
t_1 \\
t_2 \\
t_3 \\
t_4
\end{pmatrix}
[/tex]

Now separate out the different variables and see how many basis vectors this gives you.
 

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