Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $$\begin{array} { r } 3 x - 2 y + 2 z - w = 2 \\4 x + y + z + 6 w = 8 \\- 3 x + 2 y - 2 z + w = 5 \\5 x + 3 z - 2 w = 1\end{array}$$

question 77

Multiple Choice

Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
- $$\begin{array} { r } 3 x - 2 y + 2 z - w = 2 \\4 x + y + z + 6 w = 8 \\- 3 x + 2 y - 2 z + w = 5 \\5 x + 3 z - 2 w = 1\end{array}$$

• A) \(\varnothing\)
• B) \(\left\{ \left( 2,0 , - \frac { 3 } { 37 } , \frac { 9 } { 37 } \right) \right\}\)
• C) \(\left\{ \left( \frac { 1 } { 2 } , 0 , - \frac { 37 } { 3 } , \frac { 37 } { 9 } \right) \right\}\)
• D) \(\left\{ \left( 1 , - \frac { 1 } { 3 } , \frac { 4 } { 9 } , 6 \right) \right\}\)

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Definitions:

Binding Price Ceiling

A maximum price set by the government below the equilibrium price, causing shortages.

Lower Quality

Refers to products or services that do not meet the expected standards or performance criteria compared to others in the market.

Price Ceilings

Legally imposed maximum prices on goods or services that aim to keep them affordable for consumers, which can lead to shortages if set below the market equilibrium.

Black Markets

Illegal trading systems where goods or services are bought and sold at prices not regulated by the government, often in violation of price controls or rationing.