Write the system of equations corresponding to each...

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$$
\left[\begin{array}{cc|c}
{1} & {-3} & {-2} \\
{2} & {-5} & {5}
\end{array}\right] \quad R_{2}=-2 r_{1}+r_{2}
$$

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Key Concepts

Augmented Matrix

An augmented matrix is a compact way to represent a system of linear equations by combining the coefficients of the variables and the constants from the equations into one matrix. This format allows for systematic manipulation of the system through matrix operations, which is particularly useful in techniques such as Gaussian elimination.

System of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. These are often represented in an augmented matrix form which encapsulates both the coefficients of the variables and the constant terms, making it easier to apply algebraic methods to find the solutions.

Elementary Row Operations

Elementary row operations are basic manipulations such as swapping rows, scaling rows, and adding multiples of one row to another. These operations are vital in the process of transforming an augmented matrix into a simpler form (e.g., row echelon form), which helps in solving the system of linear equations without altering the solution set.

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