[2 Let A= 2 Find the characteristic polynomial. Find the eigenvalues. Find an eigenvector for each eigenvalue. Find a matrix P?

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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7.
Let A=
2 2
2 -1
Find the characteristic polynomial. Find the eigenvalues.
Find an eigenvector for each eigenvalue. Find a matrix P?
Transcribed Image Text:7. Let A= 2 2 2 -1 Find the characteristic polynomial. Find the eigenvalues. Find an eigenvector for each eigenvalue. Find a matrix P?
(2) Area of Triangle
in es
A=11√ of Triangle formed by V' and W
A (11012) BC21014) ((|12₁k)| area = 1
AB = (20₁1) - (11012)
= (1/₁0(-1)
7
AC =/ (112₁K) - (11012)
(0₁2, (²-2) (1) p
Area = 1₂11 ABXAC² ||
HỂ XÁC
12 JE
пискунорнор
=- 0 1 -1
0 2 K-2
= V
= 2^[ (K-2)+₂)
-ĴEO] HE COL
kî
let X₁ = K
X₂=-2K
So [ %/1] = K[ -=¹2₂]
in on
So eigen Vector 2 =-2 15
=-2 15 [12]
Row
] VG =
2√6
لمكات
Transcribed Image Text:(2) Area of Triangle in es A=11√ of Triangle formed by V' and W A (11012) BC21014) ((|12₁k)| area = 1 AB = (20₁1) - (11012) = (1/₁0(-1) 7 AC =/ (112₁K) - (11012) (0₁2, (²-2) (1) p Area = 1₂11 ABXAC² || HỂ XÁC 12 JE пискунорнор =- 0 1 -1 0 2 K-2 = V = 2^[ (K-2)+₂) -ĴEO] HE COL kî let X₁ = K X₂=-2K So [ %/1] = K[ -=¹2₂] in on So eigen Vector 2 =-2 15 =-2 15 [12] Row ] VG = 2√6 لمكات
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