Find Eigen value numerical questions

Q1 what is eigen vale of  of matrix A.

          A=  -1    4
               4    -1



(a)3,5

(b)-3,-5

(c)-3,5

(d)3,-5




sum of eigen value=sum of trace =-2
product of eigen value=determinant of A=-1*-1-4*4=-15

so 
(d) option is correct
because
3-5=-2
and 
3*-5=-15

Q2 What is Eigen value of matrix
               A=9   -2
                -2    6

 




sum of eigen value=9+6=15
product of eigen value=9*6- -2*-2=54-4=50

so eigen value 
10,5
because sum is 10+5=15
because product is 10*5=50

Q3.  Find eigen value of matrix

           H= 9   -2
             -2    6
if one eigen value is 5 then find other eigen value.





sum of eigen value=9+6=15
product of eigen value=9*6- -2*-2=50

if one eigen value is 5
then other is 10 
because
10*5=50
and
10+5=15

Q4. Find the eigen vale of 

           A=1  4
             3  2





sum of eigen value=2+1=3
product of eigen value=1*2-4*3=-10

so eigen value is 
5,-2
because 
5-2=3
5*-2=10

Q5. Find the eigen value of
                       A=0   1
                        -2  -3






.sum of eigen value=0-3=-3
product of eigen value=0*-3-1*-2=2
 so eigen value is -1,-2
-1-2=-3
-1*-2=2