Find the Inverse of the Matrix A, If It Exists $$A = \left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$$

question 29

Multiple Choice

Find the inverse of the matrix A, if it exists.
- $$A = \left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$$

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

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Definitions:

Primary Hypothesis

The initial theory or proposition that a research study aims to test, often focused on a specific predicted outcome.

Null Hypothesis

A statement in hypothesis testing that assumes no significant difference or effect, serving as the default assumption to be tested against an alternate hypothesis.

Independent Variable

The variable in an experiment that is manipulated or changed by the researcher to observe its effects on the dependent variable.

Cross-Sectional Study

A type of observational study that analyzes data from a population at a specific point in time.