Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 6 & - 3 & 6 & - 4 \\6 & - 2 & - 4 & - 3 \\12 & - 5 & 2 & - 7 \\0 & - 6 & 12 & 0\end{array} \right]$$

question 121

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 6 & - 3 & 6 & - 4 \\6 & - 2 & - 4 & - 3 \\12 & - 5 & 2 & - 7 \\0 & - 6 & 12 & 0\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r r r }
• \frac { 1 } { 6 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } & - \frac { 1 } { 4 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 2 } & - \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 5 } & \frac { 1 } { 2 } & - \frac { 1 } { 7 } \\
• 0 & - \frac { 1 } { 6 } & \frac { 1 } { 12 } & 0
• \end{array} \right]\]
• B) The inverse does not exist.
• C)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 6 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } & - \frac { 1 } { 4 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 2 } & - 4 & - \frac { 1 } { 3 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 5 } & \frac { 1 } { 2 } & - \frac { 1 } { 7 } \\
• 0 & - \frac { 1 } { 6 } & \frac { 1 } { 12 } & 0
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { r r r r }
• 1 & 0 & 0 & - \frac { 2 } { 3 } \\
• 0 & 1 & 0 & - \frac { 1 } { 4 } \\
• 0 & 0 & 1 & - \frac { 1 } { 8 } \\
• 0 & 0 & 0 & 0
• \end{array} \right]\]

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Definitions:

Frustration

A feeling of distress or annoyance stemming from being blocked in achieving a goal.

Perfectionist

An individual who strives for flawlessness, setting exceedingly high performance standards, accompanied by overly critical self-evaluations and concerns regarding others' evaluations.

Equally Attractive Alternatives

Situations where an individual is presented with two or more options that are perceived to be equally desirable and difficult to choose between.

Frustration

An emotional response to opposition, related to anger, annoyance, and disappointment, because a person's body or goals are being blocked.