Please answer all parts, thank you! (A) Let A= [2 0 6; -1 8 5; 1 -2 1] b= [10; 3; 3] and let W be the set of all linear combinations of the columns of A. Show that the third column of A is in W. (B) Suppose the solution set of a certain system of linear equations can be described as: x1= 3(x4), x2= 8+ x4, x3= 2-5(x4), with x4 free. Use vectors to describe this set as a "line" in R4.
Please answer all parts, thank you! (A) Let A= [2 0 6; -1 8 5; 1 -2 1] b= [10; 3; 3] and let W be the set of all linear combinations of the columns of A. Show that the third column of A is in W. (B) Suppose the solution set of a certain system of linear equations can be described as: x1= 3(x4), x2= 8+ x4, x3= 2-5(x4), with x4 free. Use vectors to describe this set as a "line" in R4.
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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![Please answer all parts, thank you!
(A) Let A= [2 0 6; -1 8 5; 1 -2 1] b=
[10; 3; 3] and let W be the set of
all linear combinations of the
columns of A. Show that the third
column of A is in W.
(B) Suppose the solution set of a
certain system of linear equations
can be described as:
x1= 3(x4), x2= 8+ x4, x3= 2- 5(x4),
with x4 free. Use vectors to
describe this set as a "line" in R4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28e7be30-eca9-4147-a850-5833b744a665%2F7f20830f-2bdd-4f47-ac18-e0b638c8e686%2Fl0w3dl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Please answer all parts, thank you!
(A) Let A= [2 0 6; -1 8 5; 1 -2 1] b=
[10; 3; 3] and let W be the set of
all linear combinations of the
columns of A. Show that the third
column of A is in W.
(B) Suppose the solution set of a
certain system of linear equations
can be described as:
x1= 3(x4), x2= 8+ x4, x3= 2- 5(x4),
with x4 free. Use vectors to
describe this set as a "line" in R4.
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