Determine the Inverse of the Given Matrix, If Possible $A=\left[\begin{array}{rrrr}-5 & 5 & 3 & -4 \\0 & 1 & -2 & 0 \\3 & 2 & 1 & 3 \\0 & 1 & 1 & 0\end{array}\right]$

question 37

Multiple Choice

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
- $A=\left[\begin{array}{rrrr}-5 & 5 & 3 & -4 \\0 & 1 & -2 & 0 \\3 & 2 & 1 & 3 \\0 & 1 & 1 & 0\end{array}\right]$

• A)\(A^{-1}=\left[\begin{array}{rrrr}
• -1 & -\frac{10}{9} & -\frac{4}{3} & -\frac{59}{9} \\
• 0 & -\frac{1}{3} & 0 & -\frac{2}{3} \\
• 0 & \frac{1}{3} & 0 & -\frac{1}{3} \\
• 1 & \frac{11}{9} & \frac{5}{3} & \frac{64}{9}
• \end{array}\right]\)
• B)\(A^{-1}=\left[\begin{array}{rrrr}
• -1 & \frac{10}{9} & -\frac{4}{3} & \frac{59}{9} \\
• 0 & \frac{1}{3} & 0 & \frac{2}{3} \\
• 0 & -\frac{1}{3} & 0 & \frac{1}{3} \\
• 1 & -\frac{11}{9} & \frac{5}{3} & -\frac{64}{9}
• \end{array}\right]\)
• C)\(\text { Singular matrix }\)
• D)\(A^{-1}=\left[\begin{array}{cccc}
• 1 & \frac{10}{9} & \frac{4}{3} & \frac{59}{9} \\
• 0 & \frac{1}{3} & 0 & \frac{2}{3} \\
• 0 & -\frac{1}{3} & 0 & \frac{1}{3} \\
• -1 & -\frac{11}{9} & -\frac{5}{3} & -\frac{64}{9}
• \end{array}\right]\)

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Definitions:

Conservation

The principle in cognitive development that recognizes the amount of a substance remains the same despite changes in its shape or container.

Theory of Mind

A cognitive skill that enables individuals to understand that others have their own thoughts, feelings, and perspectives, distinct from one's own.

Zone of Proximal Development

The range of tasks that are too difficult for an individual to master alone but can be learned with guidance and assistance from a more knowledgeable person.

Schemata

Cognitive structures that help individuals organize and interpret information in the world around them.