# Let c1, c2, ,cn R, and let A = (aij) be an n Times n matrix such

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Let c1, c2, ... ,cn R, and let A = (aij) be an n Times n
matrix such that aij = Cj for all i, j {1, 2, ,n}. Find the
eigenvalues of A.
Solution
For a matrix such as this, the corresponding characteristic
polynomial will always be
xn-(c1+c2+...+cn)xn-1=xn-1(x-(c1+c2+...+cn).
We know that setting the characteristic polynomial equal to
zero enables us to find the eigenvalues of a matrix. In this
case, letting
xn-1(x-(c1+c2+...+cn)=0
Tells us that x=0, x=c1+c2+...+cn are roots of the
characteristic equation. It follows that the eigenvalues of A
are 0 and c1+c2+...+cn.

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Let c1, c2, ... ,cn R, and let A = (aij) be an n Times n matrix such that aij = Cj for all i, j {1, 2, ,n}. Find the eigenvalues of A. Solution For a matrix such as this, the corresponding characteristic polynomial will always be xn-(c1+c2+...+cn)xn-1=xn-1(x-(c1+c2+...+cn). We know that setting th ...
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