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Homework Help: Matrices and Operations

  1. Jan 14, 2010 #1
    Let A be a n x m matrix. Show that if the function y = f(x) defined for m x 1 matrices x by y = Ax satisfies the linearity property, then f(aw + bz) = af(w) + bf(z) for any real numbers a and b and any m x 1 matrices w and z.



    Matrix Multiplication, vector addition, scalar-vector multiplication



    Scalars - k1, k2
    Vectors - u, v
    Matrix - n x m matrix

    f(aw + bz) = af(w) + bf(z)
    A(k1u + k2v) = k1Au + k2Av

    m x 1 matrices are the vectors u and v

    multiplying scalars to vectors:
    mk1 x k1 matrix
    mk2 x k2 matrix



    I'm not understanding how I am supposed to prove that this function is linear.
     
  2. jcsd
  3. Jan 14, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Write the definition of Ax in terms of index summation for A and x.
     
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