Question

The matrix [−1320−69] has eigenvalues λ_{1}=−1 and
λ_{2}=−3.

Find eigenvectors corresponding to these eigenvalues. v⃗ 1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ and v⃗ 2= ⎡⎣⎢⎢ ⎤⎦⎥⎥

Find the solution to the linear system of differential equations
[x′_{1} x′_{2}]=[−13 20−6 9][x_{1}
x_{2}] satisfying the initial conditions
[x_{1}(0)x_{2}(0)]=[6−9].

x_{1}(t)= ______ x_{2}(t)= _____

Answer #1

Find the characteristic equation and the eigenvalues (and
corresponding eigenvectors) of the matrix. 0 −3 5 −4 4 −10 0 0
4
(a) the characteristic equation (b) the eigenvalues (Enter your
answers from smallest to largest.) (λ1, λ2, λ3) = the corresponding
eigenvectors x1 = x2 = x3 =

Find the eigenvalues and the eigenvectors corresponding to them
of the matrix
-2
1
3
0
-2
6
0
0
4

Show that the matrix is not diagonalizable.
3
−4
3
0
3
3
0
0
4
Find the eigenvectors x1 and
x2 corresponding to λ1 and
λ2, respectively.
x1
=
x2
=

Find all eigenvectors of this 3x3 matrix, when the eigenvalues
are lambda = 1, 2, 3
4
0
1
-2
1
0
-2
0
1

Find all eigenvalues and eigenvectors for the 3x3 matrix
A= 1 3 2
-1 2 1
4 -1 -1

find all eigenvalues and eigenvectors of the given matrix
A= [3 2 2
1 4 1
-2 -4 -1]

find the eigenvalues of the following matrix. then find the
corresponding eigenvector(s) of one ofthose eigenvalues (pick your
favorite).
1 -2 0
-1 1 -1
0 -2 1

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.

Find the 3 * 3 matrix A corresponding to orthogonal projection
onto the solution
space of the system below.
2x + 3y + z = 0;
x - 3y - z = 0:
Your solution should contain the following information: (a) The
eigenvector(s) of
A that is (are) contained in the solution space; (b) The
eigenvector(s) of A that
is (are) perpendicular to the solution space; (c) The corresponding
eigenvalues for
those eigenvectors.

dy/dt = x- (1/2)y
dy/dt =2x +3y
a)matrix form
b)find eigenvalues/eigenvectors
c)genreal solution

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