![\[T_1 z = \frac{z + 2}{z + 3}, \qquad T_2 z = \frac z{z + 1},\]](http://latex.artofproblemsolving.com/b/7/2/b72b5e302cecdf2649c43a078aea3aa9a88ef2cc.png)
find 
and 
be a polynomial of degree 
with only real zeros and real coefficients.
we have 
.
be an 
square matrix with eigenvalues 
(each 
having algebraic multiplicity 
,
)
be a polynomial. It is known that if 
is an eigenvalue of 
is an eigenvalue of 
.
(counting multiplicities)?
(with multiplicity 3),
(with multiplicity 2),
(with multiplicity 1),
(with multiplicity 3), 
(with multiplicity 2), and 
(with multiplicity 1)?
vs. equation 
)
Y by
Q) I am trying to prove the following result attached in the pdf .
But in the last step I got a matrix of
but how could I contradicts that there is no non trivial solution of the system of equation. so that only solution is the each coefficient must be zero to get independent set proof
need help how to do.
But in the last step I got a matrix of
but how could I contradicts that there is no non trivial solution of the system of equation. so that only solution is the each coefficient must be zero to get independent set proofneed help how to do.
