• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Linear Algebra With Applications
Found in: Page 55
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Consider a linear transformation T from R2 to R2. Suppose that v and w are two arbitrary vectors in R2 and that x is a third vector whose endpoint is on the line segment connecting the endpoints of v and w. Is the endpoint of the vectorT(x) necessarily on the line segment connecting the endpoints of T(v) and T(w) ? Justify your answer.

Thus, we can say that T(x)=T(v)+k(T(w)-T(v))Is on line segment.

See the step by step solution

Step by Step Solution

Step by step Explanation Step1: Assuming the equation

We can write x=v+k(w-v) where k is any scalar between 0 and 1.

Step2: Linear Transformation

A transformation from RmRn is said to be linear if the following condition holds:

  1. Identity of Rm should be mapped to identity of role="math" localid="1659717675430" Rn.
  2. T(a+b)=T(a)+T(b) For all a,bRm.
  3. T(ca)=cT(a) Where c is any scalar and aRm.

Step3: Solving the equations

On a similar basis we can write


Thus, we can say that T(x)=T(v)+k(T(w)-T(v)) Is on line segment.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.