Question

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) = {{{ ["}}

Answer 1

Given matrin ** [4] To find eigen value of eigen vector let ņa 3 [lli 4 2 characteristic poly of A is det (A-dI) 20 ire 1-d 3 4 20 2-d (1-2) (2-2)=12=0 2-2-22 +22-1270 d-37-10=0 d2-52+27-1020 (8-5)+2(8-5) 20 (d-5) (272)=0 desão, atro das do-2 eigen value of A are 5 -2 > i) To find eigen space correst ponding to dias

consider the system CA-d,I) x20 CA-51)x=0 {[: .]-SCO - 2 [:]][] {[:] [:]}{7:6: 1-5 3-0 lol 4-0 12 2-5 [36] 0 4 consider Augmented matrix [Alo 4 3 pe 4 -3 R2 + R system becomes - 4244392=0 -424 = -392 24 = -392 -4

24 = 322 4 puk Ngahut, TER 2 423 (40) 2 42 3ut Ergen space corresponding to dias Eldu: 8134 1 ter] {•[4]loer t 3 E(d): C rresponding to Q22-2 To find eigen space corresponding consider the system (A-d27)x=0 (A-L-2))x=0 C:7-3040 [u :] [: ]][*]:07 {Lu -2

4 [*]S]0 1:20 consider the Augmented matsin is [ALOS 3 107 4 4 1 / 2 [,; st P2 'T R2-R [1: system becomes zutagro 24.-22 Put TER azat, 42-4 eigen space corresponding to do 2-2 Eldas a {[i] 1468} = {x[i]lter]

Elda) [1] option o D is correct