SOLUTION: Find eigen value corresponds to eigne vector [3 2]t for M = [1 -3] [-2 2]

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Question 1172374: Find eigen value corresponds to eigne vector [3 2]t for M = [1 -3]
[-2 2]
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the given matrix M acts on the given vector [3,2]^t.


In other words, calculate the vector


    %28matrix%282%2C1%2C++x%2Cy%29%29 = %28matrix%282%2C2%2C+1%2C-3%2C++-2%2C2%29%29.%28matrix%282%2C1%2C+3%2C2%29%29.



Since the given vector is eigenvalue vector

      (by the way, notice how I write this word --- and LEARN/memorize it (!) )


the resulting vector will be proportional to the given vector:


    the resulting vector  %28matrix%282%2C1%2C++x%2Cy%29%29 = k+%2A+%28matrix%282%2C1%2C++3%2C2%29%29.



The proportionality coefficient "k" in this equation is the eigenvalue you are seeking for.

After my explanations,  boldly go forward and  do the rest on your own.