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

---

Definitions:

Fixed Manufacturing Overhead

This refers to the consistent costs associated with the manufacturing process that do not vary with the level of production, such as salaries of managers and depreciation of factory equipment.

Overapplied

A situation where the allocated manufacturing overhead cost is greater than the actual overhead incurred.

Volume Variance

A measurement of the difference between the expected volume of production and the actual volume produced, impacting costs.

Cost

The expenditure incurred by a business to produce, acquire, or maintain a good or service.