​Solve the System of Linear Equations​ $$\left\{ \begin{array} { l l } 9 x + 9 y + 9 z & = 1 \\27 x + 45 y + 36 z & = - 3 \\27 x + 54 y + 45 z & = 2\end{array} \right.$$

question 31

Multiple Choice

​Solve the system of linear equations​ $$\left\{ \begin{array} { l l } 9 x + 9 y + 9 z & = 1 \\27 x + 45 y + 36 z & = - 3 \\27 x + 54 y + 45 z & = 2\end{array} \right.$$ ​using the inverse matrix $$\frac { 1 } { 9 } \left[ \begin{array} { c c c } 1 & 1 & - 1 \\- 3 & 2 & - 1 \\3 & - 3 & 2\end{array} \right]$$ .

• A)​ \[\left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 5 } { 9 } \\\\
• \frac { - 2 } { 3 } \\\\
• \frac { 4 } { 9 }
• \end{array} \right]\]
• B)​ \[\left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { - 4 } { 9 } \\\\
• \frac { - 11 } { 9 } \\\\
• \frac { 16 } { 9 }
• \end{array} \right]\]
• C)​ \[\left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { - 11 } { 9 } \\\\\
• \frac { 16 } { 9 } \\\\
• \frac { - 4 } { 9 }
• \end{array} \right]\]
• D)​ \[\left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 5 } { 9 } \\\\
• \frac { 1 } { 3 } \\\\
• \frac { - 2 } { 9 }
• \end{array} \right]\]
• E)​ \[\left[ \begin{array} { l }
• x \\
• y \\
• z
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 16 } { 9 } \\\\
• \frac { - 4 } { 9 } \\\\
• \frac { - 11 } { 9 }
• \end{array} \right]\]

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Definitions:

Equal Variances

An assumption in some statistical tests that the variances in the groups being compared are similar.

Normally Distributed

A symmetric probability distribution centered around the mean, demonstrating that occurrences near the mean happen more often than those at a distance.

Population Variances

A measure of how data points in a population are spread out, indicating the variability of the entire population.

Confidence Interval Estimate

An interval estimate is a range of values used to estimate a population parameter, typically defined by two numbers between which a population parameter is said to lie with a certain level of confidence.