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Linear Algebra With Applications
Found in: Page 53
Linear Algebra With Applications

Linear Algebra With Applications

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

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Short Answer

Use the concept of a linear transformation in terms of the formula y=Ax, and interpret simple linear transformations geometrically. Find the inverse of a linear transformation from localid="1659964769815" 2 to 2 to (if it exists). Find the matrix of a linear transformation column by column.

Consider the transformations from 3 to 3 defined in Exercises 1 through 3. Which of these transformations are linear?

  1. y1=2x2y2=x2+2y3=2x2

The given transformationy1=2x2y2=x2+2y3=2x2 is not linear.

See the step by step solution

Step by Step Solution

Step1: System of equations

We have given that system of equation is .y1=2x2y2=x2+2y3=2x2

For the transformation of R3to R3 it can be written as:


Step2: Linear Transformation

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

  1. Identity of Rm should be mapped to identity of Rn .
  2. For all T(a+b)=T(a)+T(b).

3. T(ca)=cT(a)Where c is any scalar and aRm

Step 3: Checking for linear transformation

Identity of R3 is (0,0,0).

Now we will find the transformation of identity element.


First condition of linear transformation does not hold.

Thus, it is not a linear transformation.

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