In each of Problems 16 through 25, find all eigenvalues and
eigenvectors of the given matrix....
In each of Problems 16 through 25, find all eigenvalues and
eigenvectors of the given matrix. 16) A= ( 1st row 5 −1 2nd row 3
1) 23) A= (1st row 3 2 2, 2nd row 1 4 1 , 3rd row -2 -4 -1)
Let A be an n x n matrix satisfying A2=A
(idempotent). Find all eigenvalues and eigenvectors of A.
I know that the eigenvalues are 0 and 1 -- I do not know how to
find the eigenvectors.
Find the characteristic equation and the eigenvalues (and
corresponding eigenvectors) of the matrix. 2 −2 5 0 3 −2 0 −1 2 (a)
the characteristic equation (b) the eigenvalues (Enter your answers
from smallest to largest.) (λ1, λ2, λ3) = the corresponding
eigenvectors x1 = x2 = x3 =
Find all distinct (real or complex) eigenvalues of A.
Then find the basic eigenvectors of A corresponding to
each eigenvalue.
For each eigenvalue, specify the number of basic eigenvectors
corresponding to that eigenvalue, then enter the eigenvalue
followed by the basic eigenvectors corresponding to that
eigenvalue.
A = 11 −10
17 −15
Number of distinct eigenvalues: ?
Number of Vectors: ?
? : {???}
Verify that the three eigenvectors found for the two eigenvalues
of the matrix in that example are linearly independent and find the
components of the vector i = ( 1 , 0 , 0 ) in the
basis consisting of them. Using
\begin{vmatrix}1 & 0 & 0 \\ -4 & 7 & 2 \\ 10
& -15 & -4\end{vmatrix}
Which of these is the answer?
(2,−5,2)(2,−5,2)
(−1,3,23)(−1,3,23)
(1,−3,32)(1,−3,32)