For the matrix M=([2,0,-1],[0,3,0],[-1,0,2])
(a) List the eigenvalues in increasing order, including any that are repeated. For example, if they are 1,1 and 0, you would enter 0,1,1
(b) Enter a basis for the eigenspace that corresponds to the lowest eigenvalue. For example, if the basis is {(1,2),(3,4)}, you would enter 1,2 3,4
(c) Enter a basis for the eigenspace that corresponds to the highest eigenvalue. For example, if the basis is {(1,2),(3,4)}, you would enter 1,2 3,4
(d) Find a matrix P such that P^(-1)MP=D, where D is a diagonal matrix. For this question, order your eigenvalues from lowest to greatest, that is λ_(1)<=λ_(2)<=λ_(3).
To enter a matrix click on the 3x3 grid of squares below. Next select the exact size of the matrix you want. Then change the entries in the matrix to the entries of your answer. If you need to start over then click on the trash can.
For the matrix M
0 3 0
2
(a) List the eigenvalues in increasing order, including any that are repeated. For example, if they are 1,1 and 0, you would enter 0,1,1
(b) Enter a basis for the eigenspace that corresponds to the lowest eigenvalue. For example, if the basis is {1,2),3,4}, you would enter [1,2],[3,4]
(c) Enter a basis for the eigenspace that corresponds to the highest eigenvalue. For example, if the basis is {(1, 2) , (3, 4)}, you would enter [1,2],[3,4]
8v 5 ZY 5 IY To enter a matrix click on the 3x3 grid of squares below. Next select the exact size of the matrix you want. Then change the entries in the matrix to the entries of your answer. If you need to start over then click on the trash can.
sin (a)
a Ox
8
a
S
?
