Find a Matrix a Such That W = Col A $\left\{ \mathrm { p } _ { 1 } , \mathrm { p } _ { 2 } , \mathrm { p } _ { 3 } \right\}$

question 9

Multiple Choice

Find a matrix A such that W = Col A.
-A: The set $\left\{ \mathrm { p } _ { 1 } , \mathrm { p } _ { 2 } , \mathrm { p } _ { 3 } \right\}$ where $\mathrm { p } _ { 1 } ( \mathrm { t } ) = 1 , \mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } , \mathrm { p } _ { 3 } ( \mathrm { t } ) = 1 + 5 \mathrm { t }$
B: The set $\left\{ p _ { 1 } , p _ { 2 } , p _ { 3 } \right\}$ where $p _ { 1 } ( t ) = t , p _ { 2 } ( t ) = t ^ { 2 } , p _ { 3 } ( t ) = 2 t + 5 t ^ { 2 }$
$C :$ The set $\left\{ \mathbf { p } _ { 1 } , \mathbf { p } _ { 2 } , \mathbf { p } _ { 3 } \right\}$ where $\mathbf { p } _ { 1 } ( t ) = 1 , \mathbf { p } _ { 2 } ( t ) = t ^ { 2 } , \mathbf { p } _ { 3 } ( t ) = 1 + 5 t + t ^ { 2 }$

• A) \(A\) and \(C\)
• B) A only
• C) all of them
• D) B only
• E) C only

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Definitions:

Consumer Surplus

The discrepancy between the total price consumers are prepared and can afford to pay for a product or service compared to the actual amount they end up paying.

Producer Surplus

The difference between what producers are willing to sell a good for and the actual price they receive, reflecting gains from trade.

Government Revenue

The money received by government from taxes and non-tax sources to finance government expenditures.

Market Size

The total volume or value of all sales within a given market over a specific period of time.