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 54
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

Find a n×n matrix A such that Ax=3x for all x in Rn.

Matrix A will be 3I, where I identity matrix of order is n×n.

See the step by step solution

Step by Step Solution

Step by step Explanation: Step1: System of equation

We have given that Ax=3x for x all in Rn.

Which implies that x is n×1 matrix vector.

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 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: Simplification

We have Ax=3x. We can write it as


Here, we have taken the vector x is non-zero.

This implies that


Where Iis identity matrix of order n×n.

Thus, matrix A will be 3I, where identity matrix of order is n×n.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

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