Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $$\begin{array} { r } x + y + z + w = 8 \\3 x + 2 y + z + 4 w = 21 \\4 x + 4 y + 5 z + 8 w = 30 \\2 x + 3 y + 6 z + 9 w = 15\end{array}$$

question 90

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.
- $$\begin{array} { r } x + y + z + w = 8 \\3 x + 2 y + z + 4 w = 21 \\4 x + 4 y + 5 z + 8 w = 30 \\2 x + 3 y + 6 z + 9 w = 15\end{array}$$

• A) \(\{ ( - 6 w + 3,9 w + 7 , - 4 w - 2 , w ) \}\)
• B) \(\{ ( 5 w + 11 , - 3 w - 7 , - 3 w + 4 , w ) \}\)
• C) \(\{ ( - 3,16 , - 6,1 ) \}\)
• D) \(\varnothing\)

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Definitions:

Model Significant

A statistical model that achieves significance levels indicating that it provides reliable predictions or insights.

Alpha

Often used in statistics to denote the level of significance, the threshold at which the null hypothesis is rejected in hypothesis testing.

Coefficient Of Determination

A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.

Correlation Coefficient

A measure of the strength of the linear relationship between two variables.