Let v be the vector space of all 2 x 2 matrices over the field f. prove that v has dimension 4 by exhibiting a basis for v which has four elements.

See the proof below.

Step-by-step explanation:

We can define a basis of V with the following elements:

So then if we define the basis X as following:

We see the the dimension for X is 4 since the basis have a dimension of 4

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