1. A matrix A and its row echelon form A, are given by: 1 001 21 A= 3 20 000 0 121 R 1 0 0 1 2 1 AR = 0 1 0 -3/2-3-3/2 02 0 0 1 5/4 3/2 7/4 i) What is the rank of the matrix A? Explain based on AR. ii) The solutions to Ax=0 may be found from [X(1)()]" =-C[xx]". Identify 1(1), etc. and the matrix C. Explain briefly how you would find the fundamental solutions s, etc. of Ax=0. How many such solutions exist? iii) What can you say about the solutions to Ax=b, b = 0? If br = (br₁DR₂,DR3)", write the most general form of the solution to Axb, if it exists. R
1. A matrix A and its row echelon form A, are given by: 1 001 21 A= 3 20 000 0 121 R 1 0 0 1 2 1 AR = 0 1 0 -3/2-3-3/2 02 0 0 1 5/4 3/2 7/4 i) What is the rank of the matrix A? Explain based on AR. ii) The solutions to Ax=0 may be found from [X(1)()]" =-C[xx]". Identify 1(1), etc. and the matrix C. Explain briefly how you would find the fundamental solutions s, etc. of Ax=0. How many such solutions exist? iii) What can you say about the solutions to Ax=b, b = 0? If br = (br₁DR₂,DR3)", write the most general form of the solution to Axb, if it exists. R
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. A matrix A and its row echelon form A, are given by:
1 001 21
A= 3 20 000
0 121
R
1
0
0
1
2 1
AR
=
0 1 0
-3/2-3-3/2
02
0 0 1
5/4 3/2 7/4
i) What is the rank of the matrix A? Explain based on AR.
ii) The solutions to Ax=0 may be found from [X(1)()]" =-C[xx]". Identify
1(1), etc. and the matrix C. Explain briefly how you would find the fundamental solutions
s, etc. of Ax=0. How many such solutions exist?
iii) What can you say about the solutions to Ax=b, b = 0? If br = (br₁DR₂,DR3)", write the
most general form of the solution to Axb, if it exists.
R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf901a98-7a67-4324-a5db-1296fd3738bf%2F852185f7-15c3-440e-a2b1-3124990d4419%2Fr178dgg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A matrix A and its row echelon form A, are given by:
1 001 21
A= 3 20 000
0 121
R
1
0
0
1
2 1
AR
=
0 1 0
-3/2-3-3/2
02
0 0 1
5/4 3/2 7/4
i) What is the rank of the matrix A? Explain based on AR.
ii) The solutions to Ax=0 may be found from [X(1)()]" =-C[xx]". Identify
1(1), etc. and the matrix C. Explain briefly how you would find the fundamental solutions
s, etc. of Ax=0. How many such solutions exist?
iii) What can you say about the solutions to Ax=b, b = 0? If br = (br₁DR₂,DR3)", write the
most general form of the solution to Axb, if it exists.
R
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