Question

This Question: 1pl 1 of 30 (0 complete) Find a basis for the eigenspace corresponding to the eigenvalue. - 1 A= 81 - 6 1 22 6 2=7 5 A basis for the eigenspace corresponding to a = 7 is {} (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Us Enter your answer in the answer box hp

Answer 1

Find a basis for the eigen espace corresponding to the eigen value o -1 -6 2 id=7 6 2 is Sol Value 7 is null by Def" eigensface corresponding to eigen space of matrix A-7I E = N(A -70) sol' of (A-71)x} = 0 OY ,X = (24 X2, X (A-73) 1,22,255 х 0 73 o I - 6 - 6 6 20:00 2 2 - 2 to Rq = 62, + R2 Roza = 22 -R3 na 0 o Rz :) o ooo xz 0 o Thes So M Satis fy x + x - x3 = o x = Kg - xz CS Scanned with CamScanner

Thus, Null spare consists of vector NCA 172) xz - x2 for any scalass A2, A3 Hence, we have EEN( A-71) = sfon -24)sfor ( [:1-6) these vectors are Clearly Thus they form linearly independent a basis of E C Eigen space This a basis of is 0) 0 Am CS Scanned with CamScanner