hello everyone now I am here to
discuss about a trick by using this
you can able to determine very quickly
 of the eigenvalue of a given matrix
we all know that how to determine the
eigenvalue that
it is a matrix  let's
suppose this matrix is a
and a minus lambda I equal to zero by
using this we
determine the eigenvalue and this is
time taking
but when the option is given you can
easily
determine the eigenvalue by using 
simple two methods
there are two methods available
so I will discuss about that
first method is summation of eigenvalue
is equal to the summation of
diagonal element
of the matrix okay
and second method is determinant of a
equals to multiplication
of eigenvalue
these two techniques are available
so
let's discuss this so first of all
 this is more
time
consuming methods this is so summation of
eigenvalue
and summation of a diagonal element
of the matrix
okay so on the diagonal element of a matrix
what is minus 1 minus 1 three
minus one plus minus one plus three
equals to
one let let's check
which is which option is matched three
plus three six not match
twelve match minus six three plus six
and zero not match three plus six six
plus five not match
three plus minus one plus two minus one
option d is match so you can see it's
option d four option d
three plus minus one plus j plus
minus 1 minus j
3d here is option
for option d minus j 3 imaginary part
cancel
minus 1 minus 1 minus 2 1 so this is
match so that means
the appropriate eigenvalue of the matrix
is this
and second method is
determinant of a let's
minus 1 into minus 3
minus 3 into
minus 9 plus 5 into
0 plus 3 plus
27 is equal to 30 that is the answer
and next
what i say determinant of a equals to
multiplication eigenvalue
so as i already determined by the first
method that this is the
appropriate answer so i check this
i directly check check this
so for option d
option d three into minus one plus j
3 minus 1 minus j 3
multiplication of the eigenvalue i
directly
take this because i already know that
otherwise you can check this check this
and after that
doesn't mean this is the only value that
match
this so mine theory into j3 minus one
minus one from
g three plus one minus three
square
minus nine minus one
into minus 10 30
so here it is proved that this equal
that means by using this or by using
this
the option is d and this is very simple
this is less time consuming
within 60 seconds you can
able to find out the answer so that's it
