Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { r r r r } 6 & - 3 & 4 & - 3 \\6 & - 2 & - 3 & - 2 \\12 & - 5 & 1 & - 5 \\0 & - 6 & 8 & 0\end{array} \right]$$

question 188

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { r r r r } 6 & - 3 & 4 & - 3 \\6 & - 2 & - 3 & - 2 \\12 & - 5 & 1 & - 5 \\0 & - 6 & 8 & 0\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r r r }
• 1 & 0 & 0 & - \frac { 1 } { 2 } \\
• 0 & 1 & 0 & - \frac { 4 } { 17 } \\
• 0 & 0 & 1 & - \frac { 3 } { 17 } \\
• 0 & 0 & 0 & 0
• \end{array} \right]\]
• B) The inverse does not exist.
• C)
• \[\left[ \begin{array} { c c c c }
• \frac { 1 } { 6 } & - \frac { 1 } { 3 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 2 } & - 3 & - \frac { 1 } { 2 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 5 } & 1 & - \frac { 1 } { 5 } \\
• 0 & - \frac { 1 } { 6 } & \frac { 1 } { 8 } & 0
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { r r r r }
• \frac { 1 } { 6 } & - \frac { 1 } { 3 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \\
• \frac { 1 } { 6 } & - \frac { 1 } { 2 } & - \frac { 1 } { 3 } & - \frac { 1 } { 2 } \\
• \frac { 1 } { 12 } & - \frac { 1 } { 5 } & 1 & - \frac { 1 } { 5 } \\
• 0 & - \frac { 1 } { 6 } & \frac { 1 } { 8 } & 0
• \end{array} \right]\]

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Definitions:

Optogenetics

A biotechnological method that uses light to control cells within living tissue, often neurons, to precisely study and manipulate physiological processes.

Channelrhodopsin-2

A light-sensitive ion channel used in optogenetics for controlling and studying neurons with light.

Halorhodopsin

A light-activated chloride pump used in optogenetics to inhibit neurons by hyperpolarizing their membrane potential.

Spatial Summation

Addition of one graded potential to another that occur close in space.