Suppose the solution set of a system of linear equations can be described as x₁=2-5x4 x₂ = −4x4 x3 = 5 +9x4 with 4 free. a. Write the solution to this system in parametric vector form. x = +x4 b. If we let p be the particular solution of Ax=b (associated with 4 = 0) and be a solution to the related homogeneous equation Ax = 0, which of the following are true about the nonhomogeneous equation A = = b? The solution set is a line through the origin in the direction of p The solution set is a line through in the direction of The solution set is a line through in the direction of p The solution set is = tvh The solution set is a = p + tvh The solution set is a line through the origin in the direction of wh The solution set is x = vh + tp

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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- 0?
c. Which of the following are true about the homogeneous equation Ax
The solution set is =
tvh
The solution set is a line through p in the direction of v
The solution set is
= vh + tp
=
The solution set is
= p + tvh
The solution set is a line through the origin in the direction of p
The solution set is a line through the origin in the direction of un
The solution set is a line through in the direction of p
Transcribed Image Text:- 0? c. Which of the following are true about the homogeneous equation Ax The solution set is = tvh The solution set is a line through p in the direction of v The solution set is = vh + tp = The solution set is = p + tvh The solution set is a line through the origin in the direction of p The solution set is a line through the origin in the direction of un The solution set is a line through in the direction of p
Suppose the solution set of a system of linear equations can be described as
x₁ = 2-5x4
with x4 free.
a. Write the solution to this system in parametric vector form.
x =
+x4
b. If we let p be the particular solution of Ax = b (associated with 4 = 0) and be a solution
to the related homogeneous equation Ax O, which of the following are true about the
nonhomogeneous equation Ax = b?
x₂ = −4x4
x3 = 5 + 9x4
The solution set is a line through the origin in the direction of p
→
The solution set is a line through p in the direction of v
→
The solution set is a line through vn in the direction of p
The solution set is
The solution set is
= tvh
= p + tvh
The solution set is a line through the origin in the direction of vh
→
The solution set is x = vh + tp
→
Transcribed Image Text:Suppose the solution set of a system of linear equations can be described as x₁ = 2-5x4 with x4 free. a. Write the solution to this system in parametric vector form. x = +x4 b. If we let p be the particular solution of Ax = b (associated with 4 = 0) and be a solution to the related homogeneous equation Ax O, which of the following are true about the nonhomogeneous equation Ax = b? x₂ = −4x4 x3 = 5 + 9x4 The solution set is a line through the origin in the direction of p → The solution set is a line through p in the direction of v → The solution set is a line through vn in the direction of p The solution set is The solution set is = tvh = p + tvh The solution set is a line through the origin in the direction of vh → The solution set is x = vh + tp →
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