Question 20 Given that A= 12 -5 has the form A= PCP-¹, C- 0c-12²2 C OP-11 0 -3 -1 and P = Op- and P = and C= OP-[¹, 3- P= Find an invertible matrix P and matrix C of the form and C= 1 11 -4 -4 OP-C-[14] and C= a b -b a such that the given matrix

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 8AEXP
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Question 20
-3 -11
Given that A=
2 -5
has the form A= PCP ¹.
°c
and P =
°C-[1] and P-[11]
=
P=
°P-C-[1]
and C=
0
. Find an invertible matrix P and matrix C of the form
O
° P-[¹, 3]
and C=
-1
-4
P-[23] and C-[11]
=
C=
a
b
-b
a
such that the given matrix
Transcribed Image Text:Question 20 -3 -11 Given that A= 2 -5 has the form A= PCP ¹. °c and P = °C-[1] and P-[11] = P= °P-C-[1] and C= 0 . Find an invertible matrix P and matrix C of the form O ° P-[¹, 3] and C= -1 -4 P-[23] and C-[11] = C= a b -b a such that the given matrix
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