(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A is an nxn square, real matrix. Let f(x) be the characteristic polynomial, write f(x) = x^{n}- c_{1}x^{n-1}+ ... + (-1)^{r}c_{r}x^{n-r}+ ... + (-1)^{n}c_{n}

Show that c_{n-1}= [tex]\sum[/tex] det (A_{ii}) where A_{ii}is the (i,i) minor of A.

Similarly, what is the coefficient c_{r}?

2. Relevant equations

3. The attempt at a solution

I have shown that c_{1}= trace(A) and c_{n}= det(A).

c_{n-1}is the coefficient of x, so is the sum of all products involving one entry from the diagonal, would this product then be the determinant of the matrix formed by deleting the row and column that this entry is in, so A_{ii}?

If this is true, how would I express it more rigorously?

Also I'm not sure how to generalise for c_{r}.

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# Homework Help: Coefficients of characteristic polynomial (linear algebra)

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