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Multiplying Matrices
In order to multiply two matrices, the first matrix should have the same number of rows as the columns in the second matrix. (n x m and m x p)

We will still use the following three matrices do complete the example problems.

  1. If , find R.


    This problem can not be solved because the dimensions do not pair up with each other.
  2. If , find Q. Colors have been added for clarification.


    To find the entries in the product matrix…

    • Note which entry you are finding by its location on a row and a column starting from the top left corner. Think of this as a coordinate plane with the variables ‘i’ and ‘j’ standing for rows and columns, respectively.


    • The variables ‘i’ and ‘j’ are used in this lesson as a way of distinguishing locations in a matrix.

    • Take the ’i’ row from the first matrix and the ‘j’ column from the second matrix, and multiply the corresponding entries.


    • Then find the sum of those products and you have the entry for position ‘i,j’.






  3. If , find P. Colors have been added for clarification.








    Notice how the product of BC is completely different from that of the product of CB. This is why order does matter in multiplying two matrices. That is, matrix multiplication is NOT commutative.

Examples
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Example
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