Diagonalization - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 2054 Quiz 08 page uf 2) November 21, 2008 NAME suyaied Salas 6 O01 1. Let A= | —2 4 —1 |; then A is diagonalizable and has only two eigenvalues, 4 and 5. Find —2 0 3 matrices P and D which represent a diagonalization of A. Even though only one of them is used in the diagonalization, find both P-! and D7}. 2 6. 41 10 1/2 You may find it useful that | —2 0 —1 | is row equivalent to | 0 0 O |, and —2 0 -1 oo 0 aQetL 1 0 1 0 1 1 | is row equivalent to | -2 -1 -1 00 0 —2 0 -2 Show all your work. (ob fd A. seen A-Ar thine vee 6-4 ° ! “2 Ga [ooo ded: BoA = 4-4Y -1/=1-2 0 - elo o o ae o 3-4 ZO st 000 os e “4 = the hi of AWE =8 one [ts “| e| the. x, Px, au free oO 1 adage h das — sintldy , «baw tr he wl gin g ASE a ff" shed fre variations om a Hs aocwter, Sice D ont Ungere at teiha ax # haces abate, mer ti He arden i chal. we, unite He 2 vedere & A=4 uhen maby Pe sox. One Answer: Hs : ait oO te, -| Zz t 4 eo ph o 6 P=||1 Oo ! Pos L162 D= ; y 7 pis : My 6 Oo 1 | “to -) eo 5 os le