The Augmented Matrix

We will represent a system of equations by a rectangular array of numbers called an augmented matrix. Here is the augmented matrix for the above example:
Some Terminology:
  • The entries in the augmented matrix are called elements.
  • Rows run across the matrix.
  • Columns run down the matrix.
  • The diagonal of the matrix is the set of elements that starts at the top, left corner and runs diagonally down and to the right. The diagonal of the above matrix consists of the numbers 4, 1 and 2.
  • Any elements in position a are said to lie above the diagonal, and any in position b are below the diagonal:
Keep in mind the following:
  • the i-th row of the augmented matrix represents the i-th equation
  • the j-th column (to the left of the vertical line) represents the (coefficients of the) j-th variable or unknown
  • the vertical line represents the equal signs



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