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Characteristic Polynomial - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

This is the Quiz Solution of Linear Algebra. Mainly includes points are Explicit Conditionsm, Expansion Across, Equilibrium Prices, Equation, Elementary, Elementary Row etc. Key important points of tags are: Characteristic Polynomial, Factored, Eigenvalues, Odd Number, Eigenspace, Odd One, Correct Notation, Basis, Acceptable, Same

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

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sethuraman_h34rt 🇮🇳

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Math 205A Quiz 08 page 1 March 21,2008 = NAME, Svanaited, Sdufiog 30 0 1.LeeA=] 5 8 -10 5 5 —7 1A. Find the characteristic polynomial of A in factored form. ale» 2 @ B-r +0 char poly « By me (lS (3-9) s Pal? Gr) 909) + 50) 5 5 “PA = (a->)( 0% 2d - Bd 56-450) = (8-d)(0% >- “t) (3-r)(4-3)(-2) = (03)(x- -2) 1B. One of the eigenvalues of A is an odd number, the other is even. Find a basis for the ejgensp: the odd one. Show all your work. Az gras oth, He: eigtn pace her a a8 ts ef wes yond: i of dis A que Xe o™ oa ; z rahe Xy = free, lass ss 1040 2/-20 12 —5/2 | 2 2 2 it {9170 -3) 20 1/2 5/2 2LetM=| 7 4 47 9 7 |ithenRREFUMIG)s| 9 90 ol toad =1 1 (3 4 45 0000 0] 01-32 1 Find bases for each of the following: use correct notation. You may write “same as" if appropriate; for example, if the basis in (2G) were the same as for (2A) then “same as 2A” would be acceptable as the answer ta 2G. es . 2A. CoM) (te He prot ch) 2B. Nul(M) need chi d Ms > & 3 they ae ALIS X= -4x, 2x, “4 a 2 -} 3 L els i wee-tn ty Sole Ot te “gl bi dye ince e{ |e art me Oxsetree 4 2 ! 218. Nul (RRER( M)) 2C. Col(RREF(M!)) il [3 PE. Row(M) ye pub ros 2F. Row(RREF(M)) { fiewoe], [e723], foo g} Sane on 2E ) (49)