Suppose A is a matrix with characteristic polynomial p( ) =3 -
a) What is the order of the matrix A?
b) Is A invertible?
c) Is A diagonalisable?
d) Find the eigenvalues of A2
a) The characteristics
polynomial P( ) has degree n
A is of order
b)The roots of characteristic polynomial
3 - are
2
or or
A matrix is invertible
det A is exactly the product of A eigenvalues
Since the product is
Then is not invertible
c) A is diagonalisable because the characteristic polynomial can be factored into distinct linear factors
I.e 3 - 2 - )
=
d) Eigenvalues of 2 are 2, 2 and 2
Which are
and
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