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 circle graph is not a function.

step-by-step explanation:

the graph of the circle is not a function.

because for a graph to be a function, each value of x must give one value of y

in the circle, the values of x for -2< x< 2 each give 2 values of y.

hence this is not a function.