Mark each of the following statement true or false: The transformation T:

a2linetagadaW

a2linetagadaW

Answered question

2021-11-08

Mark each of the following statement true or false:
The transformation T:RnR defined by T(x) = | x | is a linear transformation.

Answer & Explanation

smallq9

smallq9

Skilled2021-11-09Added 106 answers

Step 1: GIVEN AND OBJECTIVE
We will first consider the given statement,
The transformation T:Rn R defined by T(x) =|x| is a linear transformation.
The objective is to determine the statement as true or false.
Step 2: EXPLANATION
As we know, T:x|x|R gives a norm on Rn and norm is not linear.
Since, norm satisfies the following,
|x+y|x]+|y| for all x,yRn
This implies that T is not linear.
Hence, the statement is False.

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