Chapter 6 Review and Tests


Definitions, Concepts, and Formulas Examples

6.1 Matrices and Systems of Equations

  1. Matrix. An m×n matrix is a rectangular array of numbers with m rows and n columns.

  2. Augmented matrix. The augmented matrix of a system of linear equations is a matrix whose entries are the coefficients of the variables in the system together with the constants.

  3. Elementary row operations. For an augmented matrix of a system of linear equations, the following row operations will result in the matrix of an equivalent system:

    1. Interchange any two rows.

    2. Multiply any row by a nonzero constant.

    3. Add a multiple of one row to another row.

  4. Row-echelon form and reduced row-echelon form. The elementary row operations are used to transform ...

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