Determine Whether {V₁, V₂, V₃} Is a Basis for R³ $\left\{ \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 0 \\ 1 \\ 2 \end{array} \right] \right\}$

question 11

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Given the set of vectors $\left\{ \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 0 \\ 1 \\ 2 \end{array} \right] \right\}$ , decide which of the following statements is true:
A: Set is linearly independent and spans $R ^ { 3 }$ . Set is a basis for $R ^ { 3 }$ .
B: Set is linearly independent but does not span $R ^ { 3 }$ . Set is not a basis for $R ^ { 3 }$ .
C: Set spans $\mathscr { R } ^ { 3 }$ but is not linearly independent. Set is not a basis for $R ^ { 3 }$ .
D: Set is not linearly independent and does not span $R ^ { 3 }$ . Set is not a basis for $R ^ { 3 }$ .

• A) B
• B) \(\mathrm { D }\)
• C) \(\mathrm { C }\)
• D) \(\mathrm { A }\)

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Definitions:

APS

The abbreviation for "Aggregate Planning Strategy," a process in operations management to balance production and demand over a medium-term horizon; or it could refer to "Automatic Payment System," depending on context.

Income

The financial gain earned by an individual or business, typically measured on an annual basis, coming from work, investments, or other sources.

APC

Average Propensity to Consume, which is the fraction of income that a person or economy spends rather than saving.

APS

The Average Propensity to Save, which is the proportion of total income that households plan to save rather than spend on consumption.