Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. (a) find a linear transformation t : r2→r2

(a) Find a linear transformation T : R2→R2 that (i) maps the x1-axis to itself, (ii)...

50.1K

Verified Solution

Question

Advance Math

(a) Find a linear transformation T : R2→R2 that (i) maps thex1-axis to itself, (ii) maps the x2-axis to itself, and (iii) mapsno other line through the origin to itself.

For example, the negating function (n: R2→R2 defined by n(x)=−x) satisfies (i) and (ii), but not (iii).

(b) The function that maps (x1, x2) to the perimeter of arectangle with side lengths x1 and x2 is not a linearfunction. Why?

For part (b) I can't come up with any counterexamples that showT(x+y) = T(x) + T(y) or that aT(x) = T(ax) isn't true, and when Itried to use a variables instead of numbers, I ended up showingthat it did satisfy both conditions. I'm not sure what I'mmissing.

Answer & Explanation Solved by verified expert
3.7 Ratings (473 Votes)
First    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Statistics
1.2K views

A Wisconsin resident was curious whether the color of roofing materials had any association with snow...

Biology
1.2K views

compare and contrast PIP2, PIP3 and IP3 and show/explain how to get each one in details

Physics
1.2K views

5) A solid conducting sphere of radius 2.00 cm has a charge of 8.00uC. A conducting...

Biology
1.2K views

Which of the following plants has vasculature but not seeds O A Maiden Hair Moss...

Physics
1.2K views

Then If t 1 and English U of refractive index along the line y 8...

Statistics
1.2K views

Which equation correctly show how to find the percent of tiles that are white in...

Calculus
1.2K views

Add the given vectors by components U 0 327 8 171 1 V 0 647...

Algebra
1.2K views

A bag contains blue and yellow marbles Two marbles are drawn without re lacement The...

Algebra
1.2K views

Find the fifth term and the nth term of the geometric sequence whose initial term,...

Accounting
1.2K views

Problem #2 8 Points The following balance sheet contains...

Accounting
1.2K views

You loaned your roommate $4,500 for next semesters tuition. Your roommate promised to pay you...

Accounting
1.2K views

The employee federal and state income tax and Social Security tax are optional payroll deductions....