Linear combination and Basis 
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*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. 
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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

 A: 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?
A: The dimension of the vector space $V$ is the cardinality of a basis in this vector space and it's also the maximal number of linearly independant vectors of $V$ (or the minimal number of vectors which  span $V$). Now what's the dimension of $\mathcal{M}_2(\Bbb R)$? of $\mathcal{M}_3(\Bbb R)$?  Can you take it from here?
For your second question, what's the sum of Four vectors in   that form a loop when end-to-end connected? What's this mean using the notion of linearly independant?
