2) A) would you say the set of all 2x2 matrices forms a vector space? Explain. B) Given your work above do you think the set of all mxn matrices will form a vector space? Explain. C) We defined span and looked at the span of a set of vectors geometrically and numerically working with vectors from Rn. When a set of vectors spans a space the linear combination of them generates every object in the space.  Can you think of a set of 2x2 matrices such that when you take the span of them you can generate any 2x2 matrix? (hint: think of our standard basis for R2, R3, ... etc.)

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.