Consider the matrix A given by [ 2 0 0 ] [ 0 2 3 ] [ 0 3 10 ]
(20) Find all its eigenvalues and corresponding eigenvectors. Show
your work. (+5) Write down the entire eigendecomposition (i.e. the
matrices X, Lambda, and X inverse) explicitly.
Consider the given matrix.
3
0
0
0
2
0
16
0
1
Find the eigenvalues. (Enter your answers as a comma-separated
list.)
λ = 1,2,3
Find the eigenvectors. (Enter your answers in order of the
corresponding eigenvalues, from smallest eigenvalue to
largest.)
Matrix:
Ax b
[2 1 0 0 0 | 100]
[1 1 -1 0 -1 | 0]
[-1 0 1 0 1 | 50]
[0 -1 0 1 1 | 120]
[0 1 1 -1 1 | 0]
Problem 5
Compute the solution to the original system of equations by
transforming y into x, i.e., compute x = inv(U)y.
Solution:
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I have not Idea how to do this. Please HELP!
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?
2. Given A = | 2 1 0 1 2 0 1 1 1 |.
(a) Compute eigenvalues of A.
(b) Find a basis for the eigenspace of A corresponding to each
of the eigenvalues found in part (a).
(c) Compute algebraic multiplicity and geometric multiplicity of
each eigenvalue found in part (a).
(d) Is the matrix A diagonalizable? Justify your answer