Determine whether or not the following transformation T : V → W is a linear tran

Determine whether or not the following transformation T : V → W is a linear transformation. If T is not a linear transformation, provide a counter example. If it is, then: (i) find the nullspace N(T) and nullity of T, (ii) find the range R(T) and rank of T , (iii) determine if T is one-to-one, (iv) determine if T is onto.
$$\displaystyle{T}:{R}^{{2}}→{R}^{{2}}{d}{e}{f}\in{e}{d}{b}{y}{T}{\left({x},{y}\right)}={\left({x}+{1},{y}\right)}$$

• Questions are typically answered in as fast as 30 minutes

Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Warajected53

Determining;
Step 1

Step 2