Find the Inverse of the Given Matrix, If It Exists $\left[ \begin{array} { c c c } 1 & 1 & 1 \\1 & 0 & 5 \\1 & - 1 & 1\end{array} \right]$

question 56

Multiple Choice

Find the inverse of the given matrix, if it exists.
$\left[ \begin{array} { c c c } 1 & 1 & 1 \\1 & 0 & 5 \\1 & - 1 & 1\end{array} \right]$

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

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Definitions:

Consumption Map

A graphical representation showing different combinations of goods or services that provide equal satisfaction or utility to a consumer.

Budget Line

The budget line represents the combinations of two goods that a consumer can purchase with a given budget, taking into account the prices of the goods.

Consumer Preference

Individuals' or groups' choices and priorities regarding products, services, or other consumption activities.

Indifference Curves

Graphical representations in economics, showing combinations of goods between which a consumer is indifferent, implying the same level of satisfaction or utility.