Question

Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. -6 1 4 A= 0 1 1 003 (a) the characteristic equation of A [ (b) the eigenvalues of A (Enter your answers from smallest to largest.) (21, A2, A3) -([ (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of λι - basis for the eigenspace of 12 = basis for the eigenspace of 13 =

Answer 1

loin -b 3 A-II ch 14 0 1 ON O 3 1 y O 1-) 1 3-X | A-8I) = (6-1) [11-4813-43-0] -0 +0 A-\I] = 6-6-^) (1-1(3-1) =(ab Abdaxxx2 , (3-X) Ć (-6+57?) 13-03 =(-18 +15AA3x²+bx5x²x3) I-73-212 +211-18 landIl ao M. 23 A212-18.20 The characteristic egon of A _x3_21²4211-1820) Q 3

A The * eigenvalues - 22 - 11 4118 - 1 = 0 هه ل 8-3) ( ۸-\)((-) -) خر-3 و در ۱۰ ر ولما - ا - = ( و در ا- دوم ز ) ام ۸ ر 183.3 (۸۶۱ او را راح) for saab 8 - 1 - الحلم - با ۱ و 4\ 0 3 44 1 6 سے ة O ۹ L هوى O solve BX 2 ردا او ]-[ ره ا ة 0 || 3 0 0 4

42 АЧ Х2 - одX + X3 - 43 ) X4 - 0 and anal Қо, 2. - 9 ія 3 раи я, - сок X, - | А- AI -6 У 1 1 у 1 - 1 1 3-13 о ч 1 2. 1 Solve ах - 9 - | Ч 1 Х o 1 – 4, 41, 4Ч13 - 0 Azoo and 28320

3 ч хя: 0 3°, - 4 х 411 АМ, - X Х Т. 4. 5 м, - 1 , x, - X 2 eigen space of A - E) с о - 3 д-АТ- - 9 | у Р о - -qху дX, 4 ЧА, No - 1, Ахро 2 2 - 3 2. \ ya =' and Waa2 х 3 2. — 4 x +1 А 2 - 1 \ tia®м зраи А, - :