Use the Gauss-Jordan Method to Solve the System of Equations $$\begin{array} { l } x - y + 2 z + w = 5 \\y + z = 1 \\z - w = 4\end{array}$$

question 50

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.
- $$\begin{array} { l } x - y + 2 z + w = 5 \\y + z = 1 \\z - w = 4\end{array}$$

• A) \(\{ ( - 6 - 4 w , - 3 - w , 4 + w , w ) \}\)
• B) \(\{ ( - 10 , - 4,5,1 ) \}\)
• C) \(\varnothing\)
• D) \(\{ ( - 6 , - 3,4 , \mathrm {~W} ) \}\)

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Definitions:

β-diketone

A type of organic compound containing two keto (carbonyl) groups separated by a carbon atom, often depicted as RC(=O)CH2C(=O)R'.

Enols

Molecules containing a hydroxyl group attached to a carbon atom that is double-bonded to another carbon atom.

Organic Product

A compound or substance resulting from the chemical reactions involving organic molecules.

Enol

An organic compound containing a hydroxyl group directly connected to a carbon-carbon double bond, often in equilibrium with its keto form.