Use the Gauss-Jordan Method to Solve the System of Equations $$\begin{array} { l } x + 3 y - 2 z - w = 18 \\4 x + y + z + 2 w = 22 \\- 3 x - y - 3 z - 2 w = - 11 \\x - y - 3 z - 2 w = 1\end{array}$$

question 364

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last
variable be the arbitrary variable.
- $$\begin{array} { l } x + 3 y - 2 z - w = 18 \\4 x + y + z + 2 w = 22 \\- 3 x - y - 3 z - 2 w = - 11 \\x - y - 3 z - 2 w = 1\end{array}$$

• A) \(\{ ( 3,4 , - 4,5 ) \}\)
• B) \(\{ ( 3 + w , 4 - 2 w , - 4 + 2 w , w ) \}\)
• C) \(\{ ( 2,6 , - 8,7 ) \}\)
• D) \(\{ ( 18,22 , - 11,1 ) \}\)

---

Definitions:

Tryptophan

An essential amino acid used by the body to produce serotonin and melatonin, found in various protein-rich foods.

α-Ketoacid

An organic compound containing both a ketone and a carboxylic acid group, with the ketone group located at the second position from the acid.

α-Aminoacid

A type of amino acid in which the amino group is attached to the carbon atom immediately next to the carboxyl group, forming the backbone of proteins.

Conjugated Protein

A protein that is combined with a non-protein molecule in its structure, which can affect its function or stability.