Find the Inverse of the Matrix A, If It Exists $$A = \left[ \begin{array} { r r r } 5 & - 1 & 5 \\5 & 0 & 3 \\10 & - 1 & 8\end{array} \right]$$

question 43

Multiple Choice

Find the inverse of the matrix A, if it exists.
- $$A = \left[ \begin{array} { r r r } 5 & - 1 & 5 \\5 & 0 & 3 \\10 & - 1 & 8\end{array} \right]$$

• A) \(A ^ { - 1 } = \left[ \begin{array} { c c c } 1 & 0 & \frac { 3 } { 5 } \\ 0 & 1 & - 2 \\ 0 & \frac { 4 } { 5 } & 0 \end{array} \right]\)
• B) \(A ^ { - 1 } = \left[ \begin{array} { r r r } 1 & 0 & \frac { 3 } { 5 } \\ 0 & 1 & - 2 \\ 0 & 0 & 0 \end{array} \right]\)
• C) \(A ^ { - 1 } = \left[ \begin{array} { r r r } 5 & 5 & 10 \\ - 1 & 0 & - 1 \\ 5 & 3 & 8 \end{array} \right]\)
• D) \(A ^ { - 1 }\) does not exist.

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Definitions:

Actuate

To put into motion or action, typically referring to the operation of a mechanical device or system.

Applied Voltage

The voltage that is applied across a component or circuit, initiating its operation or influencing its performance.

Delay Relays

Delay relays are electromechanical or solid-state devices designed to delay the activation of an electrical circuit for a specified period, used in various timing and control applications.

Operating States

The various conditions or modes in which a device or system can exist, such as on, off, standby, or fault.