hello everyone now let us see how to
solve this problem in an easy way
consider the matrix a is equal to
the true cross matrix is given if the
eigenvalues values or a four and eight
then find the value of x and y then in
the to cross matrix the x value and the
y value or unknown we have to find the x
and y value we know trace of the matrix
will be trace of a will be equal to sum
of eigenvalues in the to cross matrix we
will get only two eigenvalues some trace
of a trace of a the sum of diagonals
here the diagonal values are two and
wife so two plus y which is equal to sum
of eigenvalues for an e which is given
in the question itself 4 plus 8 is 12
keep Y as it is and take this to the
side we'll get Y is equal to 10 we have
found the Y value now we have to find
the x value how can we find the x value
already we know that determinant of the
matrix a will be equal to the product of
the eigenvalues so we have using that
one and find and we are we are going to
use this formally and find the value of
x determinant of a which is equal to
product of eigenvalues
determinant of a determinant of a is
cross multiply their given elements 2 y
-3 X 2 into y minus 3 into X which is
equal to product of the eigenvalues the
eigenvalues 4 and H 4 into 8 and the
next day we are simplifying it to Y
value is 10 so to eat to 10 will be 20
minus 3x which is equal to 4 into 8 will
be 32 bring this 20 this side minus 33 X
is equal to 32 minus 20 minus 3x which
is equal to 32 minus 20 will be 12
he pays X a siddhis 12 divided by minus
3 which is equal to X is equal to minus
4 the values of x and y ax minus 4 and
10 thank you
