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)
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 =
2. Find all eigenvalues and corresponding linearly independent
eigenvectors of A = [2 0 3 4] (Its a 2x2 matrix)
4. Find all eigenvalues and corresponding linearly independent
eigenvectors of A = [1 0 1 0 2 3 0 0 3] (Its's a 3x3 matrix)
6. Find all eigenvalues and corresponding eigenvectors of A =
1 2 3 0 1 2 0 0 1 .(Its a 3x3 matrix)
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 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: ?
? : {???}
eigenvalues of the matrix A = [1 3 0, 3 ?2 ?1, 0 ?1 1] are 1, ?4
and 3. express the equation of the surface x^2 ? 2y^2 + z^2 + 6xy ?
2yz = 16. How should i determine the order of the coefficient in
the form X^2/A+Y^2/B+Z^2/C=1?