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let A be n*n matrix with characteristic polynomial of the form f(x)=(x-c1)^d1.....(x-ck)^dk, that is having root cj with multiplicity dj and j=1,2...k then, c1d1+c2d2+.....ckdk will be equal to ? a) determinant of A b)rank of A c)trace of A d) none i want the explanation also.

let A be n*n matrix with characteristic polynomial of the form f(x)=(x-c1)^d1.....(x-ck)^dk, that is having root cj with multiplicity dj and j=1,2...k then, c1d1+c2d2+.....ckdk will be equal to ?
a) determinant of A
b)rank of A
c)trace of A
d) none
i want the explanation also.

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
If we see the

is sum of the roots of f(x)
In the expansion of the

about the first column there is a term

Which contributes in having coefficient of

No other term in the expansion has this because other terms has coefficients untill

if take sum of coefficients that's trace of the matrix.
so B
Arun Kumar
IIT Delhi
Askiitians Faculty

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