FIND EIGENVALUES OF 3X3 MATRIX USING SHORTCUT

• SUM OF EIGEN VALUE   = TRACE SUM OF DIAGONAL VALUE

                                                  = 1+5+1=7

• PRODUCT OF EIGEN VALUE  =  det(A)  =   determinant of A                                                                                            =  (1x5x1+1x1x3+3x1x1) - (3x5x3+1x1x1+1x1x1)

                                                            =  ( 11 - 47 ) = - 36  

         Answer (c) = -2,3,6

        beacause :- SUM              = -2+3+6= 7

                         PRODUCT    = -2x3x6 =  -36

Definition: A scalar λ is called an eigenvalue of the n × n matrix A is there is a nontrivial solution x of Ax = λx. Such an x is called an eigenvector corresponding to the eigenvalue λ.
FORE MORE EIGEN VALUE   CLICK HERE