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

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation: