Question

Question 1:

Determine the algebraic and geometric multiplicity of each eigenvalue of the matrix. 2 3 3 3 2 3 3 3 2 Identify the eigenvalue(s). Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is one distinct eigenvalue, 1 = OB. There are two distinct eigenvalues, hy and 12 (Use ascending order.) OC. There are three distinct eigenvalues, 14 , 22 = (Use ascending order.) and 13

Question 2:

Thx, will give a thumb

Answer 1

Using eigen value and eigen vector we solve the given problem.
Question - Let, A= 2 33 3 2 3 3 3 2 Let, & be the eigen values of the matrix A. Then | A-11/20 → 2-0 3 3 3 2 3 3 3 2-0 7 (2-0)[02-032-9] -3[ 312–4) -9]+3[9-3(2-d)]=0 → (2-[4-44+29] - 3[6-31-9]+3 [9-6+3720 ³(2-1) (22-4 d-5)-3(-3,1-3) + 3(3+3)=0 ³(2-2) (d2-4d_5) + 9 dtg totodão > 2d²d3_8dt4d²_1075+ 18++18=0 → -/3+6737154 +8=0 d36d²_15.-820 => 3 + d²-74²-77-81-820 » ď(2+1) -7d (d+1)-8. (x+1)=0 → (2-74-8)(x+1)0 » [12817d-8] (d+i)=0 [(0-8)+(-2)] (0+1)=0 → (d+i) (4-8)(d+1]2=0 (+1) ²(d-8)=0 .. (4+1)220 "darlo1 ²da8 when darl (3 vector Cornes ponding to the eigen value dari d-8=o Let, aa be the eigen

Axe-12 2 3 3 24 ta 22 23 3 3 2 → 224 +382 +38₂ 34 + 2x2 + 3x3 34 + 3x2 + 2x₂ .24 X2 23 1 224+ 372 373 2-24 34 +222 + 3x3 = -22 324 + 3x2 + 273 = -23 3 from @ 224 +372+ 373 = -24 ² 3 4 +382 +3X320 Froom ② 34 + 2x2+3x₂=-22 > 34 + 3x2 + 3x3 = from ③ 3x+3x2+2x3 = -23 3277 372 +373 = 0 → 3(+*+ *9) 20 4+2 272320 Let, R2 = C, Azad Then 24 ocad . LE --(5)-(4-39-67 : 0(!) + (2) (0) = (3 Let, cal, firest second eigen vectors (02) =/ eigen rector eigen vector dal, second

when das Ly Let, x= ( value 6 be the eigen vector Cornesponding to the eigen dag. Then Axe 82 у 2 2 2 32 3 332 15 8. 16 Хg 8 ху Э/ 2*4+ 31, +374 3 х + 2х5 + 3 т. 3 x + 3xst 276 а ( 36 8 x 24 + 31, +3+ х = 8 го – 3*, +34 = 814-2, - 33, +31 = 6, - 5 + Х = 2хү +6 3а, 127, +31, 81 23, +36 : Бя, = 4 + х = 235 7) substracting 9 from 6 Хs txs a 2XA + 2х 4 +х, а 16-14 = 2(~4 - хв) а X4 = хос froom ③ X5+xce 274 - X4 + 6 = 2х4 - аса ау 4 = Ь Let, Then ag=a6=b let, bal Ке- № 22 ( (3) - (E) - (2) (1) be the eigen Vector Corresponding tigen Value

da8. when, da'-1, 2 and I dentify the eigen rates © There are two distinct eigen Valves di FED], 12-18 Determine the algeleric multiplicity The algebraic multiplicites of d, anda are Determine the geometric multiplicity Bases for the eigenspaces of it, and de are B [{(3). (7) and 1}[/] (0 and li (2 The geometrie multiplicities of d, and dy are Question 2 - 7 0-8 2 g 8 Let, B= o=1 Oo9 Let, d be the eigen value of the matric Then (Brill=0 → 700-8 2 gad 8 0 0 90/ 50 60 (9-1) (9.1) (7-2) = da 9,9,7 Let, na 24 22 be the eigen vector Corresponding to the eigen value dag 2 1 1 Then Baaga ㅋ ( 70-8 29 8 Oo9 (3) 91

74 -8N3 974 214+9 42 + 8 x3 973 ->)- ( . 982 943) 714-88z = 94 234 +972 +823=982 983=993 > - 883 = 4224 => 242-483 Let, ng = C, 22=0 Then 4= -40 2 ( 시 x2 12 (99-639726 x3) Let, Ca1, 14= 09 dal, U, - (8) when dat Let, az ( 15 no be the eigen rector rector Cormesponding to the eigen values d= 7 24 Then 205 ( 7 0 -8 2 g 8 o og ()+( 1)-( → 784-826 2x4+995 +826 724 725 726 (l 916 916 = 726 74 - 826=784 X6 =0 224 +995 +886 = 785 -215 → 44 = -15 214 to a let, br25 24 zob Let, aa Let, bal, Uz = .

D is the diagonalize the following matrix. 700 Ogo The lineanly independent eigen vectores of Bare (3) -(179.01) Then pa Po [] Po (979). [ A)