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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