Question
/1 1 ... 1 | 22 ... 2 Prob. 6. (12pts) Consider the non-zero n x...
/1 1 ... 1 | 22 ... 2 Prob. 6. (12pts) Consider the non-zero n x n matrix A = In n ...n (a) Find all eigenvalues of A and specify their multiplicities. Explain your reasoning.
Answers
Lets check what Eigen value comes for different n Let n=2 so A= ( 2 į] (A-21] = ['?? 221 0 = (1-2) (2-2)-1 o=2+2²-32-2 o=7²-37-D 0 = 2(2-3) 0=2(2-(172)) ; 2=0 m = 1 7= 3m Let n = 3x3 A = 2 2 2 1 L 3 3 3 TAZIP = 22-2 2 1 D r1-2 l L 3 3 3-21 = 2² [a-(1+2+3)],; 2=0 m=2 let n=4x4 2=6 m=1 Arril 1617 - 2 2 2 62 L 3 3 3 63 느타나나 1A2I1 = 7012-(1+2+3+4),: 2-0 MP3 Scanned with CamScanner >=10m=1as we have testes for n x n matrix 2 2 - 2 ---2 A = n so r 1-2 I 1.-.-1 A-21=1 ? 2-22--- 3 3 3-2----3 S It 2+ 3 + ---th 1A911=0= pant (2-(1+2+3---1)] Let calculate 1. by arithmetic progression Sum= ņ [261) + (n-1)017 =ņ [2 + nal] - I la+n] - nonto 2 so ant ca-ncht) = 0 anto or a- nen+1)=0 2= nint) multiplicit40) 2 nintl CS Scanndwe camaldiplicity (n-1)
![Lets check what Eigen value comes for different n Let n=2 so A= ( 2 į] (A-21] = [?? 221 0 = (1-2) (2-2)-1 o=2+2²-32-2 o=7²-3](http://img.homeworklib.com/questions/c3b26060-c7b9-11eb-bc67-e1bba0513db5.png?x-oss-process=image/resize,w_560)
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