Solve the Problem $W$ Is the Set of All Vectors of the Form

question 33

Multiple Choice

Solve the problem.
- $W$ is the set of all vectors of the form $\left[ \begin{array} { c } a - 4 b \\ 5 \\ 4 a + b \\ - a - b \end{array} \right]$ , where $a$ and $b$ are arbitrary real numbers.

• A)
• \(\left[ \begin{array} { r } 1 \\ 0 \\ 4 \\ - 1 \end{array} \right] , \left[ \begin{array} { r } - 4 \\ 5 \\ 1 \\ - 1 \end{array} \right]\)
• B) Not a vector space
• C)
• \[\left[ \begin{array} { r }
• 1 \\
• 0 \\
• 4 \\
• - 1
• \end{array} \right] , \left[ \begin{array} { r }
• - 4 \\
• 0 \\
• 1 \\
• - 1
• \end{array} \right] , \left[ \begin{array} { l }
• 0 \\
• 5 \\
• 0 \\
• 0
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { r }
• 1 \\
• 5 \\
• 4 \\
• - 1
• \end{array} \right] , \left[ \begin{array} { r }
• - 4 \\
• 0 \\
• 1 \\
• - 1
• \end{array} \right]\]

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Definitions:

Psychosis

A mental state characterized by a disconnection from reality, which may involve delusions, hallucinations, incoherence, and disorganized thought.

Persecutory Delusions

False, persistent beliefs that one is being pursued by other people.

Somatic Delusions

False beliefs that something is physically wrong with the individual, despite evidence to the contrary.

Delusions of Grandeur

A false belief in one's superiority, omnipotence, or importance, often observed in psychiatric conditions.