A system of linear equations can be described in a matrix equation Ax = b with 2 -1 1] 2,x = |y| and b = |b2 5 4. A = |1 1 L-1 \b3. 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
A system of linear equations can be described in a matrix equation Ax = b with 2 -1 1] 2,x = |y| and b = |b2 5 4. A = |1 1 L-1 \b3. 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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Please help me to solve questions a until d
![A system of linear equations can be described in a matrix equation Ax = b
with
[ 2
A =
L-1
El
-1
1]
2, x = |y| and b = |b2
4]
1
1
Lb3-
a. Determine if the columns of the matrix A span Rº. 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.
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63c81cc2-10ee-4f29-8ace-8d893d334c4f%2F03998be1-03e2-4ef9-b4cb-73bb1df8f49d%2Fw537ou_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A system of linear equations can be described in a matrix equation Ax = b
with
[ 2
A =
L-1
El
-1
1]
2, x = |y| and b = |b2
4]
1
1
Lb3-
a. Determine if the columns of the matrix A span Rº. 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.
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
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