Question: Let A be a 2 Ã 2 matrix, and call a line through the origin of R2 invariant under A if Ax lies on the

Let A be a 2 Ã— 2 matrix, and call a line through the origin of R2 invariant under A if Ax lies on the line when x does. Find equations for all lines in R2, if any, that are invariant under the given matrix.
(a)

(b)

2 0 0

Step by Step Solution

★★★★★

3.51 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The vectors Ax and x will lie on the same line throug... 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

Document Format (1 attachment)

938-M-L-A-E (1355).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let e be a line through the origin in R2, Pl the linear transformation that projects a vector onto l, and Fl the transformation that reflects a vector in l. (a) Draw diagrams to show that Fl is...

Let L R2 be a line through the origin, and let b 6 R2 be any point. (a) Find a geometrical construction of the closest point x e L to b when distance is measured in the standard Euclidean norm. (b)...

Let L R2 be a line through the origin in the direction of the unit vector u. (a) Prove that the matrix representative of reflection through L is R = 2uuT - 1. (b) Find the corresponding formula for...

5.1 please only write on paper. no explanation needed. Questions: 1,3,5,7,9, 25 on paper 5.1 Eigenvalues and Eigenvectors 299 Exercise Set 5.1 In Exercises 1-4, confirm by multiplication that x is an...

6. Disprove the following statement: If A is an invertible matrix, then A and A- have the same eigenvalues. 7. Let A = 2. Call a line through the origin of R' invariant under A if Ax lies on the line...

Code the function greedy_predicator without using numpy/pandas Please include explanation of the code & the computational complexity To see the description of the function: Scroll down the...

Could use some help in under 40 minutes thank you Let A be a 2 x 2 matrix with eigenvalues 3 and , and corresponding eigenvectors v.= and v, = Complete parts (a) through (c). An attractor A repeller...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Find a basis for the eigenspace corresponding to the eigenvalue. - 12 J A = 14 ,2=3 3 -39 A basis for the eigenspace corresponding to 2 = 3 is {} (Type a vector or list of vectors. Type an integer or...

Royal Essentials, Inc. began operations on January 1, 2008. The company produces a hand and body lotion in an eight-ounce bottle called Eternal Beauty. The lotion is sold wholesale in 12-bottle cases...

Evaluate/Calculate Value 1.Coin[floor(0.17 * length(Coin))] 2 .Die [floor(0.17 * length(Die))] 3 .index(Y, W) 4 .D[length(D)] 5 .length(join(Alph, -)) 6 .charAt(concat(slice(F, 2, 5), slice(X, 1,...

In the high-level programming language that your school has chosen to use, write and run two short programs, one using a count-controlled loop and the other a condition-controlled loop. They should...

10. Due to domestic instability, suppose Ukraine experiences significant capital flight. Use the Three-Sector Model to explain the effects of capital flight on Ukraines real interest rate, quantity...

Prove that if a matrix B has a left inverse, the columns of B are linearly independent.

Given Which column vectors of A correspond to the lead variables of U? These column vectors form a basis for the column space of A. Write each of the remaining column vectors of A as a linear...

If a matrix U is in row echelon form, show that the nonzero row vectors of U form a basis for the row space of U.

A bond is currently priced at $95.1, and face value is $100. The bond pays annual coupon interest of 5%. The bond matures in 6 years from today. You plan to hold the bond for 4 years and then sell....

Every year, Americans fill out their tax return forms (this year, Tax Day was moved until May 17).A new tax preparation company wanted to advertise that their company would save the average...

Chimnesia has 2 equal-sized groups of people: smokers and nonsmokers. Both types of people have utility U=ln(C) where C is the amount of consumption that people have in any given period. So long as...