Problem 2. Consider the weighted digraph given by v2 v5 a1 [wi] vị a4[w4] az[w2] • a3[w3] → V3 V4 Let A be the incidence matrix and let b = [1 2 1 1 0]'. (a) Show that Aw = b is inconsistent without doing any row-reductions or any computer calculations. Hint. The consistency of Aw = b hinges on whether or not b e Col(A) = Null(AT)-. Start by finding a basis of Null(AT). (6) Find the least squares approximate solution w to Aw = b. Here, you may use a computer but you must explain your reasoning.
Problem 2. Consider the weighted digraph given by v2 v5 a1 [wi] vị a4[w4] az[w2] • a3[w3] → V3 V4 Let A be the incidence matrix and let b = [1 2 1 1 0]'. (a) Show that Aw = b is inconsistent without doing any row-reductions or any computer calculations. Hint. The consistency of Aw = b hinges on whether or not b e Col(A) = Null(AT)-. Start by finding a basis of Null(AT). (6) Find the least squares approximate solution w to Aw = b. Here, you may use a computer but you must explain your reasoning.
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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![Problem 2. Consider the weighted digraph given by
V2
V5
a1[wi]
V1
a4[wa]
a2[w2]
V3
az[w3] →
V4
[1 2 1 1 0]".
Let A be the incidence matrix and let b
b is inconsistent without doing any row-reductions or any computer calculations.
= b hinges on whether or not b E Col(A) = Null(AT)+. Start by finding
(a) Show that Aw
Hint. The consistency of Aw
a basis of Null(AT).
%3|
(6) Find the least squares approximate solution w to Aw
must explain your reasoning.
b. Here, you may use a computer but you](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab0d92e6-c6dd-4793-90ce-ce8bc6fbfa3a%2F2fdb14ca-5286-4d11-85bc-6439ad73cca7%2Fgm6c1i8_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2. Consider the weighted digraph given by
V2
V5
a1[wi]
V1
a4[wa]
a2[w2]
V3
az[w3] →
V4
[1 2 1 1 0]".
Let A be the incidence matrix and let b
b is inconsistent without doing any row-reductions or any computer calculations.
= b hinges on whether or not b E Col(A) = Null(AT)+. Start by finding
(a) Show that Aw
Hint. The consistency of Aw
a basis of Null(AT).
%3|
(6) Find the least squares approximate solution w to Aw
must explain your reasoning.
b. Here, you may use a computer but you
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