Find the characteristic equation of A, the eigenvalues
of A, and a basis for the eigenspace...
Find the characteristic equation of A, the eigenvalues
of A, and a basis for the eigenspace corresponding to each
eigenvalue.
A =
−2
1
6
0
1
1
0
0
9
I found the eigenvalues to be (-2, 1,9).
How do I find the basis for the eigenspace corresponding to each
eigenvalue?
(c) a basis for the eigenspace corresponding to each eigenvalue
The matrix A=
1
0
0
-1
0
0
1
1
1
3x3 matrix
has two...
The matrix A=
1
0
0
-1
0
0
1
1
1
3x3 matrix
has two real eigenvalues, one of multiplicity 11 and one of
multiplicity 22. Find the eigenvalues and a basis of each
eigenspace.
λ1 =..........? has multiplicity 1, with a basis of
.............?
λ2 =..........? has multiplicity 2, with a basis of
.............?
Find two eigenvalues and basis.
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8,...
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8, 10, 12}, and C
= {4, 5, 6, 7, 8, 9, 10}.
Determine the following sets:
i. (A ∩ B) − C
ii. (A − B) ⋃ (B − C)
Consider the following second-order differential equation:
?"(?)−?′(?)−6?(?)=?(?)
(1) Let ?(?)=−12e^t. Find the general solution to the...
Consider the following second-order differential equation:
?"(?)−?′(?)−6?(?)=?(?)
(1) Let ?(?)=−12e^t. Find the general solution to the above
equation.
(2) Let ?(?)=−12.
a) Convert the above second-order differential equation into a
system of first-order differential equations.
b) For your system of first-order differential equations in part
a), find the characteristic equation, eigenvalues and their
associated eigenvectors.
c) Find the equilibrium for your system of first-order
differential equations. Draw a phase diagram to illustrate the
stability property of the equilibrium.
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.
2. For each
3*3 matrix and each eigenvalue below construct a basis for the
eigenspace Eλ.
A=...
2. For each
3*3 matrix and each eigenvalue below construct a basis for the
eigenspace Eλ.
A= (9 42 -30 -4 -25 20
-4 -28 23),λ = 1,3
A= (2 -27 18 0 -7 6 0 -9 8) , λ = −1,2
3. Construct a 2×2
matrix with eigenvectors(4 3) and (−3 −2) with eigen-values 2 and
−3, respectively.
4. Let A be the 6*6
diagonal matrix below. For each eigenvalue, compute the
multiplicity of λ as a root of the...