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Grade: 12th pass

                        

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.

6 years ago

Answers : (1)

Arun Kumar
IIT Delhi
askIITians Faculty
256 Points
							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
6 years ago
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