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How to Multiply a Matrix

A matrix can be defined as a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules. This article discusses how to multiply two matrices.

Instructions

    • 1

      A matrix looks like:
      1 3 4
      2 1 7
      Rows: The row is the set of numbers in a straight line horizontally.
      Columns: The column is the set of numbers vertically.

    • 2

      To multiply two matrices, make sure that the number of columns in the first matrix equals the number of rows in the second matrix. This MUST be the case in order to multiply two matrices.

    • 3

      Multiply the elements of each row of the first matrix by the elements of each column in the second matrix. Or to put this in more specific terms:

    • 4

      Let A be an m X n matrix and let B be an n X k matrix. To find the element in the i(th) row and the j(th) column of the product matrix AB, multiply each element in the i(th)row of A by the corresponding element in the j(th) column of B, and then add these products. The product matrix AB is an m X k matrix.

    • 5

      The product of a 2 X 3 matrix and a 3 X 1 matrix is a 2 X 1 matrix.
      The product of a 2 X 3 matrix and a 3 X 2 matrix is a 2 X 2 matrix.
      The product of a 2 X 2 matrix and a 2 X 4 matrix is a 2 X 4 matrix.
      The product AB of two matrices can be found only if the number of columns of A is the same as the number of rows of B.
      So, you cannot multiply a 2 X 4 matrix and a 2 X 2 matrix.

    • 6

      If this is a little too complicated and time consuming, use an online matrix calculator. They're very easy:

      http://joemath.com/applets/multmat/
      http://www.easycalculation.com/matrix/matrix-multiplication.php
      http://www.bluebit.gr/matrix-calculator/matrix_multiplication.aspx

      These are 3 of the best. Just plug in the matrices and go!

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