A is an n×n matrix. Check the true statements below: A. Finding an eigenvector of A might be difficult, but checking whether a given vector

Question

A is an n×n matrix. Check the true statements below: A. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. B. A matrix A is not invertible if and only if 0 is an eigenvalue of A. C. To find the eigenvalues of A, reduce A to echelon form. D. A number c is an eigenvalue of A if and only if the equation (A−c????)x=0 has a nontrivial solution x. E. If Ax=????x for some vector x, then ???? is an eigenvalue of A.

in progress 0
Isabelle 2 months 2021-09-16T16:05:38+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-16T16:06:56+00:00

    Answer:

    ???? = Identity matrix

    ???? = c

    Step-by-step explanation:

    Remember that you are looking for a value “c”  and a vector “x” such that

    Ax = cx

    In that case “x” is an eigenvector and  “c” is an eigenvalue. Therefore if you subtract “cx” from both sides of the equality you have that

    Ax-cx = 0 ,  and    ( A – Ic )x = 0  , where ” I ”  is the identity matrix. And “c” is the eigenvalue.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )