Question

In: Math

Find the basic eigenvectors of A corresponding to the eigenvalue λ. A = −1 −3 0...

Find the basic eigenvectors of A corresponding to the eigenvalue λ.

A =

−1

−3

0

−3

−12

35

4

36

−3

9

0

9

12

−37

−4

−38

, λ =

−1

Number of Vectors: 1

⎧
⎨
⎩⎫
⎬
⎭

0

Expert Solution

milcah answered 2 years ago

2. Find all eigenvalues and corresponding linearly independent eigenvectors of A = [2 0 3 4]...

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)

(a) Find a 3×3 matrix A such that 0 is the only eigenvalue of A, and...

(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.

Find the eigenvalues with corresponding eigenvectors & show work.

Find the eigenvalues with corresponding eigenvectors & show work. 1/2 1/9 3/10 1/3 1/2 1/5 1/6 7/18 1/2

find all eigenvalues and eigenvectors of the given matrix A= [1 0 0 2 1 -2...

find all eigenvalues and eigenvectors of the given matrix A= [1 0 0 2 1 -2 3 2 1]

Find all distinct (real or complex) eigenvalues of A. Then find the basic eigenvectors of A...

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: ? ? : {???}

Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 2 −2 5...

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 =

(a) Let Λ = {λ ∈ R : 0 < λ < 1}. For each λ...

(a) Let Λ = {λ ∈ R : 0 < λ < 1}. For each λ ∈ Λ, let Aλ = {x ∈ R : −λ < x < 1/λ}. Find U λ∈Λ Aλ and ~U λ∈Λ Aλ respectively. (b) Let Λ = \ {λ ∈ R : λ > 1}. For each λ ∈ Λ, let Aλ = {x ∈ R : −λ < x < 1/λ}. Find U λ∈Λ Aλ and ~U λ∈Λ Aλ respectively.

Let A = 2 0 1 0 2 0 1 0 2 and eigenvalue λ1 =...

Let A = 2 0 1 0 2 0 1 0 2 and eigenvalue λ1 = 3 and associated eigenvector v(1) = (1, 0, 1)t . Find the second dominant eigenvalue λ2 (or the approximation to λ2) by the Wielandt Dflation method

Consider the initial value problem X′=AX, X(0)=[−4,-2], with A=[−6,0,1,−6] and X=[x(t)y(t)] (a) Find the eigenvalue λ,...

Consider the initial value problem X′=AX, X(0)=[−4,-2], with A=[−6,0,1,−6] and X=[x(t)y(t)] (a) Find the eigenvalue λ, an eigenvector V1, and a generalized eigenvector V2 for the coefficient matrix of this linear system. λ= , V1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ , V2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ $ (b) Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. X(t)=c1 ⎡⎣⎢⎢ ⎤⎦⎥⎥ + c2 ⎡⎣⎢⎢ ⎤⎦⎥⎥ (c) Solve the original initial value problem. x(t)=...

Find Eigenvalues and eigenvectors 6 -2 2 2 5 0 -2 0 7