Question 1172374
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Let the given matrix M acts on the given vector [3,2]^t.


In other words, calculate the vector


    {{{(matrix(2,1,  x,y))}}} = {{{(matrix(2,2, 1,-3,  -2,2))}}}.{{{(matrix(2,1, 3,2))}}}.



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  {{{(matrix(2,1,  x,y))}}} = {{{k * (matrix(2,1,  3,2))}}}.



The proportionality coefficient "k" in this equation is the eigenvalue you are seeking for.
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After my explanations, &nbsp;boldly go forward and &nbsp;<U>do the rest on your own</U>.