I am trying to find e-values and e-vectors of the matrix:
I found that ʎ= √2 i
Then when trying to find the e-vector I was stuck at
V= [-2-√2 i 3
How do I find V ???
Stacey Warren - Expert brainly.com
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(A-L)x = 0
(-2-√2 i)x + 3y = 0
2x+(2-√2i)y = 0
we can setup a system of equations to solve for x and y
As I took in class, I should find a value to multiply it by the first row so the first element in the 2nd row becomes 0. Then it is in row-echelon form and the rest is easy...
Sorry I mean after multiplying something by the 1st row AND ADDING to the 2nd row, the 1st element of the 2nd row should become 0
we get something like:
x = (1+i/sqrt2)y
How is that?
i take it you are not good at row reductions?
I'm not good at math! :(
im gonna use a instead of isqrt2, in either case its simply an unknown amount
swap rows, not needed but its viable
divide row 1 by -2
multiply row 1 by 2+a and add the results to row 2
0 (-1+a/2)(2+a) + 3
-1(2+a)+(a/2(2+a) + 3
-2 -a + a + a^2/2 + 3
a^2/2 + 1
now we might want to address that a = -isqrt2
(-i)^2 2/2 + 1
(-i)^2 + 1
-1 + 1 = 0
these leaves as as:
therefore: x = y(1-a/2)