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Math Help - Matrix Multiplication

  1. #1
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    Matrix Multiplication

    Let A = (aij) be an m x n matrix. Let r and s be between or equal to 1 to m. Let Irs be the matrix whose rs-composition is 1 and such that all other components are equal to 0.

    (a) What is IrsA.

    I'm totally confused, can someone explain where to begin.
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  2. #2
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    Hello millerst
    Quote Originally Posted by millerst View Post
    Let A = (aij) be an m x n matrix. Let r and s be between or equal to 1 to m. Let Irs be the matrix whose rs-composition is 1 and such that all other components are equal to 0.

    (a) What is IrsA.

    I'm totally confused, can someone explain where to begin.
    I don't know what this bit means.
    ...Let Irs be the matrix whose rs-composition is 1...
    Have you been given an explanation of this? It sounds as if I_{rs} is a binary matrix (all its elements are either 0 or 1) but more than that, I can't say.

    All I can say for sure so far, is that, if I_{rs}A is meaningful, then the number of columns in I_{rs} is the same as the number of rows in A. So I_{rs} is a l\times m matrix, for some value of l, and the order of the resulting product will be l \times n.

    Can anyone else shed any light on this?

    Grandad
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  3. #3
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    Here's my interpretation of the question.
    Quote Originally Posted by millerst View Post
    Let A = (a_{ij}) be an m x n matrix. Let r and s be between or equal to 1 to m. Let I_{rs} be the mm matrix whose (r,s)-component is 1 and such that all other components are equal to 0.

    (a) What is I_{rs}A?
    First, as Grandad says, the number of columns of I_{rs} must be the same as the number of rows of A (otherwise the product I_{rs}A is not defined). Second, I'm guessing that I_{rs} is meant to be a square matrix, so that the product I_{rs}A will have the same number of rows and columns as A.

    If the only nonzero component of I_{rs} is a 1 in row r and column s, then you should be able to see that the only nonzero components of I_{rs}A will be in row r. What's more, the element in the (r,j)-position in I_{rs}A will be the (s,j)-component of A. So row r of I_{rs}A will be the same as row s of A, and all the other rows of I_{rs}A will consist of zeros.
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