If the Set W Is a Vector Space, Find a Set

question 14

Multiple Choice

If the set W is a vector space, find a set S of vectors that spans it. Otherwise, state that W is not a vector space.
- $W$ is the set of all vectors of the form $\left[ \begin{array} { c } a + 6 b \\ 3 b \\ 4 a - b \\ - a \end{array} \right]$ , where $a$ and $b$ are arbitrary real numbers.

• A)
• \(\left[ \begin{array} { r } 1 \\ 3 \\ 4 \\ - 1 \end{array} \right] , \left[ \begin{array} { r } 6 \\ 0 \\ - 1 \\ 0 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } 1 \\ 0 \\ 4 \\ - 1 \end{array} \right] , \left[ \begin{array} { r } 6 \\ 3 \\ - 1 \\ 0 \end{array} \right]\)
• C) Not a vector space
• D)
• \[\left[ \begin{array} { l }
• 1 \\
• 0 \\
• 4 \\
• 0
• \end{array} \right] , \left[ \begin{array} { r }
• 6 \\
• 0 \\
• - 1 \\
• 0
• \end{array} \right] , \left[ \begin{array} { r }
• 0 \\
• 3 \\
• 0 \\
• - 1
• \end{array} \right]\]

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