Linear combination and Basis 
*

*Consider a set of five arbitrary 2x2 matrices. Can you always write one as a linear combination of the others? Explain. Repeat for five arbitrary 3x3 matrices.

*For each of the following sets explain whether or not the set is/could be a basis for the space mentioned.
a) Four vectors in   that form a loop when end-to-end connected. 
...............
Problem is i didnt understand the questions.
For the first question:  i know what linear combination is, but Do i have to find that five matrices? which can be linear combination of one another ? or is asking that whether any 5 matrices can be linear combination of one another or cant? 
For the second question: 
i have learned Standard basis of matrix, (actually learning) but there is no standard. Im just started learning and bit confused 
if any1 explain it little bit i will figure it out.
Thanks


The first part of the first question is asking whether every set of five $2\times 2$ contains one that is a linear combination of the other four; the second part is asking the same question about sets of five $3\times 3$ matrices. The first part can be paraphrased as follows: is every set of five $2\times 2$ matrices linearly dependent? Similarly for the second part of the first question.
The second question is asking whether four geometric vectors that form a loop can be a basis. An example of such a loop in $\Bbb R^2$ is shown here:

HINT: What’s the sum of four vectors that form a loop?
