Suppose that a 2 × 2 matrix A has eigenvalues λ = -3 and 4, with...

Suppose that a 2 × 2 matrix A has eigenvalues λ = -3 and 4, with corresponding eigenvectors [1m1]and [7,2], respectively. Find A^2.

Expert Solution

milcah answered 2 years ago

The 3 x 3 matrix A has eigenvalues 5 and 4. (a) Write the characteristic polynomial...

The 3 x 3 matrix A has eigenvalues 5 and 4. (a) Write the characteristic polynomial of A. (b) Is A diagonalizable ? Explain your answer. If A is diagonalizable, find an invertible matrix P and diagonal matrix D that diagonalize A. Matrix A : 4 0 -2 2 5 4 0 0 5

eigenvalues of the matrix A = [1 3 0, 3 ?2 ?1, 0 ?1 1] are...

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?

the matrix A=[-5,1;-21,5] has eigenvalues Г1=-2 and Г2 = 2 the basis of the eigenspace v1=[1,3]...

the matrix A=[-5,1;-21,5] has eigenvalues Г1=-2 and Г2 = 2 the basis of the eigenspace v1=[1,3] v2=[1,7] find the invertible matrix S and diagonal matrix D such that S^-1 AS=D S= D=

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 =

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

Find the values of λ (eigenvalues) for which the given problem has a nontrivial solution. Also...

Find the values of λ (eigenvalues) for which the given problem has a nontrivial solution. Also determine the corresponding nontrivial solutions (eigenfunctions). y''+2λy=0; 0<x<π, y(0)=0, y'(π)=0

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)

Find the inverse of the matrix [ 1 1 4 ] [ 3 2 4 ]...

Find the inverse of the matrix [ 1 1 4 ] [ 3 2 4 ] [ 1 1 6 ] It is a 3*3 matrix

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]

(a) Let λ be a real number. Compute A − λI. (b) Find the eigenvalues of...

(a) Let λ be a real number. Compute A − λI. (b) Find the eigenvalues of A, that is, find the values of λ for which the matrix A − λI is not invertible. (Hint: There should be exactly 2. Label the larger one λ1 and the smaller λ2.) (c) Compute the matrices A − λ1I and A − λ2I. (d) Find the eigenspace associated with λ1, that is the set of all solutions v = v1 v2 to (A...

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