Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array} { l } x - 8 y + z = 2 \\3 x - y + 2 z = 6\end{array}$

question 259

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.
$\begin{array} { l } x - 8 y + z = 2 \\3 x - y + 2 z = 6\end{array}$

• A) \(\left\{ \left( \frac { - 46 - 15 z } { 25 } , \frac { 0 + z } { 25 } , z \right) \right\}\)
• B) \(\{ ( 2,0,1 ) \}\)
• C) \(\left\{ \left( \frac { 46 - 15 z } { 23 } , \frac { 0 + z } { 23 } , z \right) \right\}\)
• D) \(\varnothing\)

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Definitions:

Observations

The individual entities or datapoints collected for research or analysis purposes, providing the basis for statistical conclusions.

Degrees Of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution or to a system, without violating any constraints.

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis, used in hypothesis testing.

Regression Coefficients

Quantitative measures in statistical models representing the change in the dependent variable for a one-unit change in an independent variable, assuming all other variables are held constant.