1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Product matrix as a Linear Combination

  1. Oct 4, 2009 #1
    Problem Statement


    [tex]\mathbf{y} = [y_1\, y_2\, ...\, y_m][/tex]


    [tex]A =
    \left[\begin{array} {cccc}

    Show that the product yA can be expressed as a linear combination of the row matrices of A
    with the scalar coefficients coming from y

    Attempt at Solution

    I thought that I would write out the actual product, which is a row vector. I thought that
    something might jump out at me from here:

    yA = [(y1a11 + y2a21 + ... + ymam1) (y1a12 + y2a22 + ... + ymam2) (y1a1n + y2a2n + ... + ymamn)]

    I am not sure where to go from here. I know that it is going to be a summation of the rows of A .... but what I have now is just written column-wise... and it is not a summation.

    A hint maybe?
  2. jcsd
  3. Oct 4, 2009 #2
    I think that you have a row vector. You can treat it just like a column vector and break it down into a sum. For example (a + b + c, d + b, b + c) = (a, d, b) + (b, b, c) + (c, 0, 0).

    Pull out terms that have the same factor from y.
  4. Oct 4, 2009 #3
    I think that I got it!

    I just wrote the summation of the rows of A :

    [a11 a12 ... a1n] + [a21 a22 ... a2n] + ... + [am1 am2 ... amn]

    and then noted that each term needs to multiplied by each of the elements of y :

    y1[a11 a12 ... a1n] + y2[a21 a22 ... a2n] + ... + ym[am1 am2 ... amn]

    I guess I just thought the solution would have been a little more 'graceful' as opposed to 'guess and check.' :yuck:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook