a) Find a 2 × 2 matrix A such that (−4, 0) and (−2, −4) are eigenvectors of A corresponding eigenvalues 9 and −7. (b). Let B be the matrix [3 2 4 1] Find the eigenvalues and corresponding eigenvectors of B. c) Find the eigenvalue of C corresponding to the eigenvector (−1, 1, 0)^t (t stands for transposition) given that C is the matrix [10 5 − 9 −9 −4 9 5 5 −4]
a) Find a 2 × 2 matrix A such that (−4, 0) and (−2, −4) are eigenvectors
of A corresponding eigenvalues 9 and −7.
(b). Let B be the matrix
[3 2
4 1]
Find the eigenvalues and corresponding eigenvectors of B.
c) Find the eigenvalue of C corresponding to the eigenvector (−1, 1, 0)^t
(t stands for transposition) given that C is the matrix
[10 5 − 9
−9 −4 9
5 5 −4]
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Where did all these values come from
part a)
Where
P=-4-20-4 and D=900-7
Now
P-1=1det(P)Adj(P)⇒P-1=116-420-4⇒P-1=18-210-2
Therefore
A=PDP-1⇒A=-4-20-4900-718-210-2⇒A=18-4-20-4-189014⇒A=1872-640-56⇒A=9-80-7
Hence the matrix
| A=9-80-7 |
Please explain part a, b, c again i cant live with the previuos explanation. Thank you!!
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