Ohio Resource Center
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Content Supports
Solving Systems of Linear Equations; Row Reduction
Discipline
Mathematics
Grades
11, 12, Postsecondary
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Professional Commentary

This site illustrates in general, and then with detailed examples, how to solve a system of equations using Gaussian elimination. Applying elementary row operations to the augmented matrix for the system of equations, the student can reduce the matrix to row-echelon form, from which the solution of the system, or the nonexistence of a solution, can easily be determined. (sw)

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Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (11–12)
D.
Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases.
Patterns, Functions and Algebra Standard
Benchmarks (11–12)
D.
Apply algebraic methods to represent and generalize problem situations involving vectors and matrices.
Grade Level Indicators (Grade 11)
7.
Model and solve problems with matrices and vectors.
9.
Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution).
Grade Level Indicators (Grade 12)
5.
Set up and solve systems of equations using matrices and graphs, with and without technology.
Principles and Standards for School Mathematics
Number and Operations Standard
Compute fluently and make reasonable estimates
Expectations (9–12)
develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
Algebra Standard
Represent and analyze mathematical situations and structures using algebraic symbols
Expectations (9–12)
judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.