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

Mark each of the following statement true or false:
The transformation $$\displaystyle{T}:{R}_{{{n}}}\rightarrow{R}$$ defined by T(x) = | x | is a linear transformation.

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Step 1: GIVEN AND OBJECTIVE
We will first consider the given statement,
The transformation $$\displaystyle{T}:{R}_{{{n}}}\rightarrow$$ 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, $$\displaystyle{T}:{x}\rightarrow{\left|{x}\right|}\in{R}$$ gives a norm on $$R_{n}$$ and norm is not linear.
Since, norm satisfies the following,
$$\displaystyle{\left|{x}+{y}\right|}\leq{\mid}{x}{]}+{\left|{y}\right|}$$ for all $$\displaystyle{x},{y}\in{R}_{{{n}}}$$
This implies that T is not linear.
Hence, the statement is False.