Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax=0 is the line in R² through (4,1) and the origin. Then, find a vector b in R² such that the solution set of Ax=b is not a line in R² parallel to the solution set of Ax=0. Why does this not contradict the theorem that states that if the equation Ax=b is consistent for some given b and p is a solution, then the solution set of Ax=b is the set of all vectors of the form w=p+Vn. where V₁ is any solution of the homogeneous equation Ax=0? Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax=0 is the line in R2 through (4,1) and the origin. Choose the correct answer below. OA. O B. 1 C. Find a vector b in R² such that the solution set of Ax=b is not a line in R2 parallel to the solution set of Ax = 0. O D.
Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax=0 is the line in R² through (4,1) and the origin. Then, find a vector b in R² such that the solution set of Ax=b is not a line in R² parallel to the solution set of Ax=0. Why does this not contradict the theorem that states that if the equation Ax=b is consistent for some given b and p is a solution, then the solution set of Ax=b is the set of all vectors of the form w=p+Vn. where V₁ is any solution of the homogeneous equation Ax=0? Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax=0 is the line in R2 through (4,1) and the origin. Choose the correct answer below. OA. O B. 1 C. Find a vector b in R² such that the solution set of Ax=b is not a line in R2 parallel to the solution set of Ax = 0. O D.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax = 0 is the line in R2 through (4,1) and the origin. Then, find a vector b in R2 such that the solution set of Ax=b is not a line in R²
parallel to the solution set of Ax = 0. Why does this not contradict the theorem that states that if the equation Ax = b is consistent for some given b and p is a solution, then the solution set of Ax=b is the set of all
vectors of the form w=p+Vh, where V₁ is any solution of the homogeneous equation Ax = 0?
O A.
Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax=0 is the line in R² through (4,1) and the origin. Choose the correct answer below.
&c.
1
- 4
*[BE]
1
-
14
O B.
(---)
1
1
4 - 4
Find a vector b in R² such that the solution set of Ax = b is not a line in R² parallel to the solution set of Ax = 0.
O D.
1 1
4 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf7838de-33b1-4c9b-b444-de4b7c84d20a%2F49180786-c50c-420f-814f-04607c0437ef%2Fk8xzrxi_processed.png&w=3840&q=75)
Transcribed Image Text:Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax = 0 is the line in R2 through (4,1) and the origin. Then, find a vector b in R2 such that the solution set of Ax=b is not a line in R²
parallel to the solution set of Ax = 0. Why does this not contradict the theorem that states that if the equation Ax = b is consistent for some given b and p is a solution, then the solution set of Ax=b is the set of all
vectors of the form w=p+Vh, where V₁ is any solution of the homogeneous equation Ax = 0?
O A.
Construct a nonzero 2x2 matrix A such that the solution set of the equation Ax=0 is the line in R² through (4,1) and the origin. Choose the correct answer below.
&c.
1
- 4
*[BE]
1
-
14
O B.
(---)
1
1
4 - 4
Find a vector b in R² such that the solution set of Ax = b is not a line in R² parallel to the solution set of Ax = 0.
O D.
1 1
4 4
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