Perform the row operation and write the equivalent system....

Perform the row operation and write the equivalent system. What did the operation accomplish?
Add -2 times Equation 1 to Equation 3.
$$\left\{\begin{aligned}
x-2 y+3 z &=5 \\
-x+3 y-5 z &=4 \\
2 x &-3 z=0
\end{aligned}\right.$$
Equation 1
Equation 2
Equation 3

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Key Concepts

Elementary Row Operations

Elementary row operations are basic manipulations applied to the rows of a system of linear equations or a matrix. These operations—such as multiplying a row by a nonzero scalar, swapping rows, or adding a multiple of one row to another—are used to simplify the system while ensuring that its solution set remains unchanged.

Equivalent Systems

An equivalent system of linear equations is one that retains the same solution set as the original system, even though its appearance may change. Using row operations to create an equivalent system is a fundamental technique in linear algebra that facilitates the solving process without altering the underlying solutions.

Gaussian Elimination

Gaussian elimination is a method used to solve systems of linear equations by performing a series of row operations to convert the system into an upper triangular or row-echelon form. This process often involves eliminating variables systematically, which simplifies the system and makes it easier to solve through back substitution.

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