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Martix and vector

  1. Mar 23, 2010 #1
    Q1:
    Let A =
    1 3 0
    0 -4 4
    3 4 5

    a) Find Cartesian equations for Col(A) and Null(A).
    b) Are the columns of A linearly independent? Give full reasons for your answer (based on
    the definition of linear independence).

    Q2: Prove that in any vector space k × 0 = 0, where k is any real number and 0 is the zero vector.

    Q3:
    The set M2,2 of 2 × 2 matrices, with real entries, is a vector space.
    The set of diagonal matrices D =
    [(a 0
    0 b) | a, b 2 E R is a subset of M2,2
    a) Write down two particular matrices which belong to D, and two particular matrices which
    belong to M2,2 but not to D.
    b) Prove that D is a subspace of M2,2
     
  2. jcsd
  3. Mar 23, 2010 #2
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