anonymous
  • anonymous
how to find the eigenvector of this 1 0 1 0 1 0 1 0 1 I have found the eigenvalues which are 0, 1, 2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
lol, um, so how did you find them?
amistre64
  • amistre64
-L along the diagonals; and take the determinant; set it equal to 0 to find Ls
amistre64
  • amistre64
hard to tell what the vectors are without a vector to go by tho ...

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amistre64
  • amistre64
Ax = Lx Ax-Lx = 0 (A-L)x = 0 and solve for x
amistre64
  • amistre64
subtract the Ls from the diags and rref to find "x"
amistre64
  • amistre64
1-0 0 1 0 1-0 0 1 0 1-0 1-1 0 1 0 1-1 0 1 0 1-1 1-2 0 1 0 1-2 0 1 0 1-2
amistre64
  • amistre64
rref{{1-0, 0, 1},{ 0, 1-0, 0},{ 1, 0, 1-0}} 1 0 1 x1 -1 0 1 0 x2 = x3 0 0 0 0 x3 1 rref{{1-1, 0, 1},{ 0, 1-1, 0},{ 1, 0, 1-1}} 100 0 001 = x3 0 000 1 rref{{1-2, 0, 1},{ 0, 1-2, 0},{ 1, 0, 1-2}} 10-1 1 01 0 = x3 0 00 0 1
amistre64
  • amistre64
im not to sure about the second one tho
anonymous
  • anonymous
I used the rule of sarus and got x^3-3x^2+2x (used x for lambda) and then i got 0, 1, 2 as eigenvalues
amistre64
  • amistre64
ill trust you did that part good then ;)
amistre64
  • amistre64
the rest is just row reducing that eugened matrixes with the 0 vector
anonymous
  • anonymous
ok thanks :)
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=%7B%7B1%2C+++0%2C++1%7D%2C%7B++0%2C+++1%2C+++0%7D%2C%7B++1%2C+++++0%2C+++1%7D%7D yeah, i missed v2 :)

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