Determine Whether {V₁, V₂, V₃} Is a Basis for R³

question 4

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Let $\mathrm { A } = \left[ \begin{array} { r r r r r } - 1 & 3 & 7 & 2 & 0 \\ 1 & - 2 & - 7 & - 1 & 3 \\ 2 & - 4 & - 9 & - 5 & 1 \\ 3 & - 6 & - 11 & - 9 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r r r } 1 & - 3 & - 7 & - 2 & 0 \\ 0 & 1 & 0 & 1 & 3 \\ 0 & 0 & 5 & - 3 & - 5 \\ 0 & 0 & 0 & 0 & 0 \end{array} \right]$
It can be shown that matrix $\mathrm { A }$ is row equivalent to matrix $\mathrm { B }$ . Find a basis for $\mathrm { Col } \mathrm {} \mathrm { A }$ .

• A)
• \(\left[ \begin{array} { l } 1 \\ 0 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { c } - 3 \\ 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { c } - 7 \\ 0 \\ 5 \\ 0 \end{array} \right]\)
• B)
• \(\left[\begin{array}{r}
• -1 \\
• 1 \\
• 2 \\
• 3
• \end{array}\right],\left[\begin{array}{r}
• 3 \\
• -2 \\
• -4 \\
• -6
• \end{array}\right],\left[\begin{array}{c}
• 7 \\
• -7 \\
• -9 \\
• -11
• \end{array}\right]\)
• C)
• \(\left[ \begin{array} { r } - 1 \\ 1 \\ 2 \\ 3 \end{array} \right] , \left[ \begin{array} { r } 3 \\ - 2 \\ - 4 \\ - 6 \end{array} \right] , \left[ \begin{array} { r } 2 \\ - 1 \\ - 5 \\ - 9 \end{array} \right]\)
• D)
• \(\left[\begin{array}{r}
• -1 \\
• 1 \\
• 2 \\
• 3
• \end{array}\right],\left[\begin{array}{r}
• 3 \\
• -2 \\
• -4 \\
• -6
• \end{array}\right],\left[\begin{array}{r}
• 7 \\
• -7 \\
• -9 \\
• -11
• \end{array}\right],\left[\begin{array}{r}
• 2 \\
• -1 \\
• -5 \\
• -9
• \end{array}\right],\left[\begin{array}{r}
• 0 \\
• 3 \\
• 1 \\
• -1
• \end{array}\right]\)

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