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Determinant Prob. (1 Viewer)

Yip

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This is kinda off-syllabus, but i was wondering how one would go about this problem:

(a) Let A be a 3x3 non-singular matrix, and I be the 3x3 identity matrix. Show that:

det(A<sup>-1</sup>-xI)=[-x<sup>3</sup>/det(A)][det(A-x<sup>-1</sup>I)]

(b) Let A=
0 1 0
0 0 1
4 -17 8
(i) Show that 4 is a root of det(A-xI)=0 and hence find the other roots in surd form
(ii) Solve det(A<sup>-1</sup>-xI)=0

I can only work out (b)(i) ~.~
thx in advance ^^

<sup> </sup>
 
Last edited:

Yip

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oh ic....~.~ that means that the roots are simply the reciprocals of the roots of (b)(i) eh...i have no clue about proving part a though ~.~ im rather new to this matrix stuff...
 

ngai

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properties of determinant that u need:
det(AB) = det(A)det(B)
det(A-1) = 1/det(A)
det(cA) = cndet(A) for A in Rn
hope uve seen those before =)

so then det(A-x-1I) / det(A)
= det((A-x-1I)A-1)
= det(I - x-1A-1)
= (-1)3det(A-1x-1 - I)
= - det(A-1 - xI) / x3
 
Last edited:

Templar

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Hmm...you returning for good, ngai, or just a temporary visit?
 

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