Find the eigenspace corresponding to each eigenvalue
of
a.
b.
c.
d.
e.
f.
Find the eigenspace corresponding to each eigenvalue of A 3 8 (5) = 8A(-2) = 4 b. A- [12] {{ }) {{}) 841-2) = {{{ z?}) 841) = {{ --]) {[ -> ]}) 843) = {{{ 2 }) ( =>]}) 842) = 812) = {{{1}) 8A(7) = d. 8A(-5) = e. 8A(-1) = 8A(-3) = f. 8A(-1) = {}}}) 844) = {{{ ["}}
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -1 6 2 16 2 -1 8 (b) Suppose that the vector z is an eigenvector of the matrix A corresponding to the eigenvalue 4. Let n be a positive integer. What is A"r equal to?
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -16 2 1 6 2 -1 8 (b) Suppose that the vector r is an eigenvector of the matrix A corresponding to the eigenvalue 1. Let n be a positive integer. What is A" equal to?
4 2 3 13. Find a basis for the eigenspace of the matrix A1 1- corresponding to the 2 49 eigenvalue -3. [4 points.]
Find the eigenspace corresponding to each eigenvalue of A A 13 4.2. O a. Ob. 8,15 = ({}) 841-2) = ({{ }}) 821-1) = {[1]). 896-3) = {{ ?]) 847) = ({}]]). 8x(+2) = {{ {"}}) ({}]]). 8(a) = ({{ }}) 84(1) = {[ -]]). 8913) - ({{ :']) ={{{1}}) od 8A(-1) = O Of. 8A(-5) = 84(2) =
Corresponding eigenvectors of each eigenvalue 9 Let 2. (as find the eigenvalues of A GA 1 -- 1 and find the or A each 5 Find the corresponding eigenspace to each eigen value of A. Moreover, Find a basis for The Corresponding eigenspace (c) Determine whether A is diagonalizable. If it is, Find a diagonal matrix ) and an invertible matrix P such that p-AP=1
Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2 The matrix A = 0 2 0 has eigenvalues X1 = 2 and X2 1 2 3 For each eigenvalue di, use the rank-nullity theorem to calculate the geometric multiplicity dim(Ex). Find the eigenvalues of A = 0 0 -1 0 0 geometric multiplicity of each eigenvalue. -7- Calculate the algebraic and
(1 point) Find a basis of the eigenspace associated with the eigenvalue 3 of the matrix 1 0 -4 2 3 4 1 0 5 A= 3 3 C Abasis for this eigenspace is 0 -2 0 0 1
3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4
3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4
3, where 4. Find a basis for the eigenspace corresponding to 4 0 1 A20 -2 0