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:

Word Recognition Method

The word recognition method is a technique used in reading instruction that focuses on the ability to recognize written words quickly and efficiently.

Transitivity

The principle that if A is greater than B in a property and B is greater than C, then A is greater than C.

Abstract Concepts

Ideas or thoughts that do not have a physical or concrete existence, but are understood through mental representation and cognitive processes.

Hypothetical Thinking

The ability to think about situations, propositions, or problems that are not based on immediate reality or current experiences.