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Linear Algebra With Applications
Found in: Page 120
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

Give an example of a linear transformation whose kernel is the plane x+2y+3z=0in 3.

The required linear transformation is,


See the step by step solution

Step by Step Solution

Step by Step Solution:  Step 1: To define kernel of linear transformation

The kernel of linear transformation is defined as follows:

The kernel of a linear transformation Tx=Ax from m to n consists of all zeros of the transformation, i.e., the solutions of the equations Tx=Ax=0

It is denoted by kerTor ker A

Step 2: To give an example of a linear transformation

We require linear transformation Asuch that

Av=0,where the plane is v=x,y,z:x+2y+3z=0is 3is the kernel of the transformation.

Since we know that the dot product of the required vector with normal vector of given plane given by,

123,is equal to 0, the required linear transformation is,


where, v=x,y,z:x+2y+3z=0

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