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 210

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:

Population Parameter

A numerical value that represents a characteristic or measure of an entire population.

Population Standard Error

A measure of how much the sample mean of a population is likely to vary from the true population mean.

Confidence Interval

An array of values, sourced from statistical analysis of a sample, believed to cover the value of an unspecified population parameter.

Mean

The average of a set of numerical values, calculated by adding all the figures together and then dividing by the number of values.