Find the Inverse, If It Exists, for the Matrix $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 2 \\ 6 & 15 & - 3 & - 4 \\ 12 & 10 & - 6 & - 2 \\ 18 & 0 & - 6 & 0 \end{array} \right]$

question 234

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 2 \\ 6 & 15 & - 3 & - 4 \\ 12 & 10 & - 6 & - 2 \\ 18 & 0 & - 6 & 0 \end{array} \right]$

• A)
• \(\left[ \begin{array} { r r r r } - \frac { 1 } { 3 } & - \frac { 3 } { 5 } & - 1 & - 2 \\ \frac { 1 } { 3 } & \frac { 2 } { 5 } & 1 & \frac { 1 } { 2 } \\ - \frac { 1 } { 3 } & - \frac { 1 } { 5 } & - 1 & - \frac { 1 } { 2 } \\ \frac { 1 } { 6 } & 0 & \frac { 1 } { 3 } & 0 \end{array} \right]\)
• B)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 3 } & - \frac { 1 } { 3 } & \frac { 1 } { 3 } & - \frac { 1 } { 6 } \\
• \frac { 3 } { 5 } & - \frac { 2 } { 5 } & \frac { 1 } { 5 } & 0 \\
• 1 & - 1 & 1 & \frac { 1 } { 3 } \\
• - \frac { 3 } { 2 } & - 1 & \frac { 1 } { 2 } & 0
• \end{array} \right]\]
• C) The inverse does not exist.
• D)
• \[\left[ \begin{array} { c c c c }
• - \frac { 1 } { 3 } & \frac { 1 } { 3 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } \\
• - \frac { 3 } { 5 } & \frac { 2 } { 5 } & - \frac { 1 } { 5 } & 0 \\
• - 1 & 1 & - 1 & \frac { 1 } { 3 } \\
• - 2 & 1 & - \frac { 1 } { 2 } & 0
• \end{array} \right]\]

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Definitions:

Normally Distributed

This describes a probability distribution that is evenly balanced around the mean, with data near the mean appearing more frequently than data at a distance from the mean.

Linear Regression

A statistical method used to model the relationship between a dependent variable and one or more independent variables, assuming a linear relationship.

Independent Variables

Variables that are manipulated or changed in an experiment to test their effects on dependent variables.

Coefficient Of Determination

A statistical measure that quantifies the proportion of the variance in the dependent variable that is predictable from the independent variable(s).