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Vector spaces and matrices question

  1. Oct 12, 2009 #1
    Massively stuck with this one, have done some reading and am having difficulty connecting matrices to vector spaces

    (a) Verify that the space of the real (2 x 2)-matrices, endowed with the standard addition
    and multiplication by real scalars, forms a vector space
    (b) Specify a basis for this vector space
    (c) What is its dimension?

    any help would be greatly appreciated.
  2. jcsd
  3. Oct 12, 2009 #2
    For (a), you must show that the properties of a vector space are satisfied. See: http://en.wikipedia.org/wiki/Vector_space#Definition

    For (b), find a set that spans this vector space (ie any vector in the space can be written as a linear combination of vectors in your spanning set). After you have done this, try to find the minimal number of vectors that can accomplish this. See: spanning set, linear independence

    For (c), The dimension of the vector space is the number of vectors in the basis.
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