Definition:Equivalent Systems of Simultaneous Linear Equations

Definition

Let $S_1$ and $S_2$ be two systems of simultaneous linear equations.

Then $S_1$ and $S_2$ are equivalent if and only if:

every solution to $S_1$ is also a solution to $S_2$

and:

every solution to $S_2$ is also a solution to $S_1$.

Sources

• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.3$ Applications to Linear Equations: Definition $1.6$