The matrix A given below has an eigenvalue A = 12. Find a basis of the eigenspace corresponding to this eigenvalue. 12 12 -12 A = 16 -4 12 How to enter a set of vectors. In order to enter a set of vectors (e.g. a spanning set or a basis) enclose entries of each vector in square brackets and separate vectors by commas. For example, if you want to enter the set of vectors 5 -1 -3 then you should do it as follows: [5,-1/3, -1], [-3/2, 0, 2], [-1, 1/2, -3] Enter a basis of the eigenspace of A corresponding to A = 12:

3 -4 One eigenvalue of the matrix A is A₁ - - 8. 33 -20 Find enough vectors to form a basis of the eigenspace of A corresponding to X₁. Fill vectors from left to right. Leave unneeded vectors blank. 181- V₁ = Question Help RU V2 V3 E

Matrix A is factored in the form PDP Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 4 A = 221 13 1 122 2 2 2 2 0 - 1 2-2 0 500 01 001 1 8 1 8 1 4 1 4 1 8 3 8 1 1 2 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) OA. There is one distinct eigenvalue, λ = O B. In ascending order, the two distinct eigenvalues are ₁ = OC. In ascending order, the three distinct eigenvalues are ₁ =₁^₂= {}, respectively. A basis for the corresponding eigenspace is { }. and 2₂ = Bases for the corresponding eigenspaces are { } and { }, respectively. {1},{1}, and and 23. Bases for the corresponding eigenspaces are =

7 Please need help, show clear work thank you.

Matrix A is factored in the form PDP - 1 Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 3 0 2 -1 0 - 1 5 0 0 1 - A = 6 5 6. 1 3 050 3 1 3 0 0 1 0 0 3 -1 0 - 1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, A =. A basis for the corresponding eigenspace is { }. B. In ascending order, the two distinct eigenvalues are , = and 12 = Bases for the corresponding eigenspaces are { and { , respectively. %3D C. In ascending order, the three distinct eigenvalues are , =, 12 = and A3 = Bases for the corresponding eigenspaces are {0{}, and {}, respectively.

Consider the given matrix. 5 -1 Find the eigenvalues. (Enter your answers as a comma-separated list.) 1 = Find a basis for each eigenspace. (Order the bases by corresponding eigenvalues, where eigenvalues are ordered from smallest to largest by real part, then by imaginary part.) |: }