Plz help me to find the answer for following question;
A matrix
Find
(a) Find Eigen valves A
(b) Egen vectors A
(c) obtain a matrix P such that is a diagonal matrix
(d) If , state the special property of each of and
(e) Using the above result reduce the quadratic from Q(x) to form Q(y) where
(f) obtain the relationship between and
Now I solved part (a) as follows
the result gain
and
part (b) solved as follows
x
then if
[tex]x
also I did for
now I need help to find rest of parts in this question, also I need to know the above calculations are in correct or not!! if some are in incorrect plz. let me know the place and how I correct it
Hi thanks for the reply and comments.
Yes I got an error the matrix A should be
In part (b) the vector means if , then we have the vector of [a,b,c] is it true? likewise , and also have vector [a,b,c] is it true?
in part (c) you mean the eigen values of A is insert to the diagonal matrix?
Plz explain me...
the result gain
Assume ur eigenvalues are right, so
For b, to find eigenvectors, sub each eigenvalues into the matrix and find the nullspace of the matrix, it should yield exactly 1 nullspace vector for each eigenvalue (for this example)
c. yes, the diagonal entries of the diagonal matrix is the eigenvalues of A
Hi thnks for the reply and help.So now we complete part (a), I approch the part (b) as follows
, the the mat will be
then according to equations and , the results shold be x=0, y=0, z=o then the vector
If , then the matrix will be
[/tex]
Then according to equations , and , results shouldbe x=0, y=3, z=-4, the vector is
again , then the equations should be , and . results are x=0, y=4, z=3
plz help me the above procedure is correct or wrong..and if wrong let me know the right answer/way..