In Problems 3133 A represents a 2 x 2 matrix 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 )

Question: In Problems 3133 A represents a 2 x 2 matrix. Show that the system x' = Ax has constant solutions other than x(t) 0

In Problems 31–33 A represents a 2 x 2 matrix.

Show that the system x' = Ax has constant solutions other than x(t) Ξ 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.)

Step by Step Solution

★★★★★

3.29 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To show that the system x Ax has constant solutions other than xt 0 if and only if there exists a co... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related First Course Differential Equations Questions!

If a vector B is a linear combination of the columns of A, show that the system AX = B is consistent (that is, it has at least one solution.)

If E is a 2 Ã 2 matrix with entries between 0 and 1, show that I - E is invertible and (I - E)-1 ¥ 0 if and only if tr E then tr E = a + d and det E = ad - bc. E =

In this exercise, we are working with the concept of an elasticity of substitution. This concept was introduced in part B of the Chapter. Thus, this entire question relates to material from part B,...

Question 6 1 pts Let A be a constant entry 3 x 3 matrix and consider the system X' = AX. Suppose X1, X2, and X3 are solutions to 1 3 1 this system with X1(2.5) = 71 ,X2 (2.5) = 1 and X3 (2.5) = 73...

1. - Expain the motivations of Unilever in acquiring Inmarko. - Identify the risks Unilever faces in using acquisition as a mode for growth, as opposed to other modes discussed in the chapter. 2....

Please find the solution to these question. Thank you so much. Student Home x Exam 1 X zy 1.7. Gauss-Jordan elimir X Weekly Assignment 3 x Principles Of Lust: S 1 x * Course Hero X + X G...

COULD YOU ANSWER THESE PROBLEMS? 1. (6 points) Consider the matrix A = 4 The only eigenvalue for the matrix is A = -1 and the only linearly independent eigenvector is v1 = [1,2]". Find the solution...

Problems : 9,11,24,25,26 Direction : in the exercices 9 and 11 find a basis for the eigenspace corresponding to each listed eigenvalueHello can I have some help here please. Can you write on a sheet...

1. Ch. 4 By using the Repeated Substitution Method only to answer the following Microeconomics question: Given the following system equations of price (P) and quantity (0) determination in a widget...

Assume these facts instead: the friend was hired to locate investors. Instead, he offered to loan the money to Stella and Molly if they could wait one year until he had access to his trust fund. In...

First Savings of Rainbow, Iowa, reported transaction deposits of $75 million (the daily average for the latest two-week reserve computation period). Its nonpersonal time deposits over the most recent...