Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 2 & - 4 & 0 & 2 \\6 & - 8 & 0 & 4 \\6 & - 16 & 0 & 6 \\0 & 0 & - 5 & 0\end{array} \right]$$

question 66

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 2 & - 4 & 0 & 2 \\6 & - 8 & 0 & 4 \\6 & - 16 & 0 & 6 \\0 & 0 & - 5 & 0\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r r r }
• - 1 & \frac { 3 } { 4 } & 0 & 3 \\
• \frac { 1 } { 2 } & 0 & 0 & - \frac { 1 } { 2 } \\
• 0 & - \frac { 1 } { 4 } & 0 & - \frac { 1 } { 2 } \\
• 0 & 0 & - \frac { 1 } { 5 } & 0
• \end{array} \right]\]
• B)
• \[\left[ \begin{array} { r r r r }
• - 1 & \frac { 1 } { 2 } & 0 & 0 \\
• \frac { 3 } { 4 } & 0 & - \frac { 1 } { 4 } & 0 \\
• 0 & 0 & 0 & - \frac { 1 } { 5 } \\
• 3 - \frac { 1 } { 2 } & - \frac { 1 } { 2 } & 0
• \end{array} \right]\]
• C)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 2 } & - \frac { 1 } { 4 } & 0 & \frac { 1 } { 2 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 8 } & 0 & \frac { 1 } { 4 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 16 } & 0 & \frac { 1 } { 6 } \\
• 0 & 0 & - \frac { 1 } { 5 } & 0
• \end{array} \right]\]
• D)
• \(\text { The inverse does not exist. }\)

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Definitions:

Congruence

Refers to the degree of agreement, harmony, or correspondence between two or more things, often used in mathematics, psychology, and interpersonal relationships.

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Social Design

The creation of social environments and structures with the purpose of improving societal relations and addressing social issues.

Principal Players

Key or leading figures in a particular context, activity, or scenario, who play a significant role in determining its outcome.