1. If (1, -1) is an eigenvector of A with associated eigenvalue -2, and (1, 1)...

1. If (1, -1) is an eigenvector of A with associated eigenvalue -2, and (1, 1) is an eigenvector of A with associated eigenvalue 4, then what the entries of A ,a11 , a12, a21 and a22 ?

2. If A has a repeated eigenvalue, the A definitely isn't diagonalizable. (True or False)

Expert Solution

milcah answered 1 year ago

1. What is the definition of an eigenvalue and eigenvector of a matrix? 2. Consider the...

1. What is the definition of an eigenvalue and eigenvector of a matrix? 2. Consider the nonhomogeneous equationy′′(t) +y′(t)−6y(t) = 6e2t. (a)Find the general solution yh(t)of the corresponding homogeneous problem. (b)Find any particular solution yp(t)of the nonhomogeneous problem using the method of undetermined Coefficients. c)Find any particular solution yp(t)of the nonhomogeneous problem using the method of variation of Parameters. (d) What is the general solution of the differential equation? 3. Consider the nonhomogeneous equationy′′(t) + 9y(t) =9cos(3t). (a)Findt he general...

If v is an eigenvector for a matrix A, can v be associated with two different...

If v is an eigenvector for a matrix A, can v be associated with two different eigenvalues? Prove your answer.

Solve the system using an eigenvalue/eigenvector approach and plot both x(t) and y(t) over a 60...

Solve the system using an eigenvalue/eigenvector approach and plot both x(t) and y(t) over a 60 minute time interval. dx/dt= 8y/200-8x/100 dy/dt=8x/100-8y/100 inital conditions: x=0, y=100, t=0

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

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How is energy an eigenvalue? Do the math. Kinetic energy= T= 1/2 mv^2 = p^2 /...

How is energy an eigenvalue? Do the math. Kinetic energy= T= 1/2 mv^2 = p^2 / 2m = h^2 / 2m Lambda^2

let A =[4 -5 2 -3] find eigenvalues of A find eigenvector of A corresponding to...

let A =[4 -5 2 -3] find eigenvalues of A find eigenvector of A corresponding to eigenvlue in part 1 find matrix D and P such A= PDP^-1 compute A^6

Let ? be an eigenvalue of a matrix A. Explain why dim(?) ? 1

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 0 0

Which of the following statements is/are true? 1) If a matrix has 0 as an eigenvalue,...

Which of the following statements is/are true? 1) If a matrix has 0 as an eigenvalue, then it is not invertible. 2) A matrix with its entries as real numbers cannot have a non-real eigenvalue. 3) Any nonzero vector will serve as an eigenvector for the identity matrix.

Estimate the lowest eigenvalue pair of matrix A using the Inverse Power Method A = 2 8...

Estimate the lowest eigenvalue pair of matrix A using the Inverse Power Method A = 2 8 10 8 4 5 10 5 7 starting with initial guess x0 = [1 1 1]T and εaλ ≤ 1%

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