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?
(a) Find a 3×3 matrix A such that 0 is the only eigenvalue of A,
and the space of eigenvectors of 0 has dimension 1. (Hint: upper
triangular matrices are your friend!)
(b) Find the general solution to x' = Ax.
PLEASE SHOW YOUR WORK CLEARLY.
for the matrix, A= [1 2 -1; 2 3 1; -1 -1 -2; 3 5 0]
a. calculate the transpose of A multiplied by A
b. find the eigenvectors and eigenvalues of the answer to a
c. Find the SVD of matrix A
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.
Use this theorem to find the inverse of the given matrix or show
that no inverse exists. (If an answer does not exist, enter DNE in
any cell.)
1
2
5
1
−1
0
2
1
2
1
−5
0
1
1
2
1