Answered: Show that the system x' =Ax has…

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...

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Question

Show that the system x' =Ax has constant solutions other
than x(t)= 0 if and only if there exists a (constant) vector
x ≠ 0 with Ax = 0. (It is shown in linear algebra that such
a vector x exists exactly when det(A) = 0.)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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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.

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