Chapter 6 Review and Tests

Review

Definitions, Concepts, and Formulas	Examples
6.1 Matrices and Systems of Equations Matrix. An $m \times n$ matrix is a rectangular array of numbers with `m` rows and `n` columns. 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. 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: Interchange any two rows. Multiply any row by a nonzero constant. Add a multiple of one row to another row. Row-echelon form and reduced row-echelon form. The elementary row operations are used to transform ...

Definitions, Concepts, and Formulas

Examples

Matrix. An $m \times n$ matrix is a rectangular array of numbers with m rows and n columns.
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.
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.
Row-echelon form and reduced row-echelon form. The elementary row operations are used to transform ...

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