Show that the system x' =Ax has constant solutions otherthan x(t)= 0 if and only if there exists a (constant) vectorx ≠ 0 with Ax = 0. (It is shown in linear algebra that sucha vector x exists exactly when det(A) = 0.)
Show that the system x' =Ax has constant solutions otherthan x(t)= 0 if and only if there exists a (constant) vectorx ≠ 0 with Ax = 0. (It is shown in linear algebra that sucha vector x exists exactly when det(A) = 0.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 68E: Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if...
Related questions
Question
Show that the system x' =Ax has constant solutions other
than x(t)= 0 if and only if there exists a (constant)
x ≠ 0 with Ax = 0. (It is shown in
a vector x exists exactly when det(A) = 0.)
Expert Solution
Step 1
Given data : x’=Ax
we have to prove that system x’=Ax has constant solution other than x(t)=0 if and only if there exists a non zero constant vector x such that Ax=0.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage