Linear Algebra. Can anyone help with vector spaces?

Pre-College Topics High School Life
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<p>I dont know where to start. Please guide me. Thanks.</p>

<li><p>Show that R^[mxn], with the usual addition and scalar multiplication of matrices, satisfies the eight axioms of a vector space.</p></li>
<li><p>Show that C[a,b], with the usual scalar multiplication and addition of functions, satisfies the eight axioms of a vector space.</p></li>
<li><p>Show that the element 0 (vector) in a vector space is unique.</p></li>
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<p>I really don’t know how to start these. I have the eight axioms in front of me. Can someone describe the process for each of these in detail to help me out? Thanks.</p>

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<p>Anyone help?</p>

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<p>linear alg already? how old are you =
im finishing calc this summer and starting linear alg / diff eq.</p>

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<p>yeah i’m not starting linear algebra until this semester either… sorry</p>

<p>ftc123- you’re finishing BC calc or calc 3? cause calc 3 is a prereq. for diff equ.</p>

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<ol>
<li>(I’m assuming R is an m x n matrix). Basically, all you have to do is show that any m x n matrix satisfies the eight (or ten, as I learned it) axioms of vector spaces, for example, where V and W are in the set of m x n matrices: V + W is in the set; V + W = W + V…etc.</li>
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<p>calc 3 (10 char)</p>

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<p>

Yes, there are eight axioms with two closure properties. The object must satisfy both closure properties before they can satisfy the eight axioms.</p>

<p>Can my m x n matrix be a n by 1 matrix to make things easier? So I don’t have to show all operations done on a m x n matrix using all the letters and subscripts?</p>

<p>Let X = (x1,x2,x3,…xn)T and let Y = (y1,y2,y3,…yn) then:</p>

<p>Axiom 1: (x1+y1, x2+y2, x3+y3, xn+yn)T = (y1+x1, y2+x2, y3+x3, yn+xn)T</p>

<p>Then I would continue with the remaining seven axioms?</p>

<p>NOTE: The “T” indicates a transpose of the vector to allow it to show column vectors only.</p>