(2) Area of Triangle A=11* Of Triangle formed by V' and W in es =√6 A (11012) BC21014) ((|12₁k)| area = 1 AB = (2100) - (11012) = (1/₁10 (-1) 2 7 (0₁2, (²-2) ()- p AC =/ (112₁K) - (11012) = Area = 1/₂ 11ABXAC² || [ VE = ² пискунорнор 2√6 =V let X₁ = K X₂=-2K HỂ XÁC IT TË =- 0 1 -1 0 2 K-2 => [ (K-2)12) -ĴEO] HE COL kî So [ %/1] = K[ -=¹2₂] So eigen Vector 2 = -2 15 [12] 7 how

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 16EQ
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(2) Area of Triangle
A=11√ of Triangle formed by V' and W
A (11012) BC21014) ((|12₁k)| area = 1
AB = (20₁1) - (11012)
= (1/₁0(-1)
AC =/ (112₁K) - (11012)
Area = 1₂11 ABXAC² ||
пискунорнор
] VG =
2√6
in es
7
(0₁2, (²-2) (1) p
= V
let X₁ = K
X₂=-2K
HỂ XÁC
12 JE
لمكات
=- 0 1 -1
0 2 K-2
= 2^[ (K-2)+₂)
-ĴEO] HE COL
kî
So [ %/1] = K[ -=¹2₂]
in on
So eigen Vector 2 =-2 15
=-2 15 [12]
Row
Transcribed Image Text:(2) Area of Triangle A=11√ of Triangle formed by V' and W A (11012) BC21014) ((|12₁k)| area = 1 AB = (20₁1) - (11012) = (1/₁0(-1) AC =/ (112₁K) - (11012) Area = 1₂11 ABXAC² || пискунорнор ] VG = 2√6 in es 7 (0₁2, (²-2) (1) p = V let X₁ = K X₂=-2K HỂ XÁC 12 JE لمكات =- 0 1 -1 0 2 K-2 = 2^[ (K-2)+₂) -ĴEO] HE COL kî So [ %/1] = K[ -=¹2₂] in on So eigen Vector 2 =-2 15 =-2 15 [12] Row
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?
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