Question
Asked Oct 1, 2019
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Please see the attachment. Linear Algebra

( 2)
F
a
(4) Let A
Define the trace of A, denoted tr(A), to be ad.
C
(a) Show that the characterisic polynomial of A is:
2 tr(A)Adet(A)
(b) Show that for A as
above,
A2 tr(A) A det(A) I2 0
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( 2) F a (4) Let A Define the trace of A, denoted tr(A), to be ad. C (a) Show that the characterisic polynomial of A is: 2 tr(A)Adet(A) (b) Show that for A as above, A2 tr(A) A det(A) I2 0

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Expert Answer

Step 1

Given matrix is

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A = d C

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Step 2

Trace and determinant of matrix is defined as

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tr(A) sum of diagonal entries tr(A) a d det(A) ad -bc

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Step 3

(a)The characteristic polynomial of...

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a-AI b | A- AI d AI | A-AIaI(d -AI)-bc | A-AIad -a+d)+ -bc | A-AI2-a+d)+ (ad -bc) | A -AI tr(A)A+det(A)

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