1. A system of linear equations can be described in a matrix equation Ax = b with [2 -1 1] A = |1 1 2, x L-1 5 4] and b = |b2 a. Determine if the columns of the matrix A span R³. Give your arguments. b. If the system is homogeneous, describe the trivial solution of the system (if any) in parametric vector form. Also, give a geometric description of the solution set. Give the clear argument. c. If the system is nonhomogeneous and consistent, describe b in parametric vector form. Give the clear argument. d. If b, = 5,b2 = -3, b3 = 0, is the system consistent? Give valid argument. Find the solution set of the system. Compare the solution set with the trivial solution of the homogeneous system in b.
1. A system of linear equations can be described in a matrix equation Ax = b with [2 -1 1] A = |1 1 2, x L-1 5 4] and b = |b2 a. Determine if the columns of the matrix A span R³. Give your arguments. b. If the system is homogeneous, describe the trivial solution of the system (if any) in parametric vector form. Also, give a geometric description of the solution set. Give the clear argument. c. If the system is nonhomogeneous and consistent, describe b in parametric vector form. Give the clear argument. d. If b, = 5,b2 = -3, b3 = 0, is the system consistent? Give valid argument. Find the solution set of the system. Compare the solution set with the trivial solution of the homogeneous system in b.
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 system of linear equations can be described in a matrix equation Ax = b
with
2 -1 1]
A = |1 1 2,x = |y| and b = |b2
[-1 5 4]
a. Determine if the columns of the matrix A span R³. Give your arguments.
b. If the system is homogeneous, describe the trivial solution of the system
(if any) in parametric vector form. Also, give a geometric description of
the solution set. Give the clear argument.
c. If the system is nonhomogeneous and consistent, describe b in parametric
vector form. Give the clear argument.
d. If b, = 5, b2 = -3, bz = 0, is the system consistent? Give valid argument.
Find the solution set of the system. Compare the solution set with the
trivial solution of the homogeneous system in b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22ade8df-aeab-4f4b-b08f-74c3640cc3d0%2Ff0673af4-ac42-4855-b662-a520d814f3bf%2Fzyof2p_processed.png&w=3840&q=75)
Transcribed Image Text:1. A system of linear equations can be described in a matrix equation Ax = b
with
2 -1 1]
A = |1 1 2,x = |y| and b = |b2
[-1 5 4]
a. Determine if the columns of the matrix A span R³. Give your arguments.
b. If the system is homogeneous, describe the trivial solution of the system
(if any) in parametric vector form. Also, give a geometric description of
the solution set. Give the clear argument.
c. If the system is nonhomogeneous and consistent, describe b in parametric
vector form. Give the clear argument.
d. If b, = 5, b2 = -3, bz = 0, is the system consistent? Give valid argument.
Find the solution set of the system. Compare the solution set with the
trivial solution of the homogeneous system in b.
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