I am stuck. I got this far and it looks like when I did Row Reduction I reached the Identity Matrix, which should mean 8 is not an eigenvalue. But when I put that in as an answer I am wrong. I cannot see where I made a mistake, and I still need to find the eigenvalue.

HW 51 70-27 Is 1 = 8 an eigenvalue of 2 7 2 / ? If so, find one - 4 3 6 1 corresponding eigenvector. Ax - 2X = 0 A is matrix, a is sealor so we can't math those directly Ax- 1x = 0 ( A - 2 ) x = 0 contmath A $ 2 ( A - 2I)x = O use identity matrix 70 - 2 1 180 0 1 10 0] A = 2 7 2 - 1080 I = 1010 2:8 -4 3 61 10 0 8 0 0 1 1- 10 -2 - 2 0 - 4 would be 2 RI + 12 2 only trivial 2 -1 2 2 -1 2 Solution so not eigen vale -4 3 - 2 0 - 1 - 2 10 2 1- IRI 4 0 8 6 - 1 - 2 -7R3 - 4 3 2 - 4 3 2 3 10 10 2 7 - 1R2 0 - 3 - 6 0 1 2 - 3RETR 0 3 10 0 3 10 14 10 2 0 1 2 0 0 470-2 Is * = 8 an eigenvalue of 2 7 2 ? If so, find one corresponding eigenvector. -43 6