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elementary_operations_on_a_linear_system
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If we perform one of the following operations on a system of linear equations:
- list the equations in a different order; or
- multiply one of the equations by a non-zero real number; or
- replace equation $j$ by “equation $j$ ${}+{}$ $c\times {}$ (equation $i$)”, where $c$ is a non-zero real number,
then the new system will have exactly the same solutions as the original system. These are called elementary operations* on the linear system.
Why do elementary operations leave the solutions of systems unchanged?
- we are doing the same thing to the left hand side and the right hand side of each equation, so any solution to the original system will also be a solution to the new system; and
- these operations are reversible, using operations of the same type, so any solution to the new system will also be a solution to the original system.
elementary_operations_on_a_linear_system.1453658163.txt.gz · Last modified: by rupert