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

---

Definitions:

Stimulus Package

A set of government spending policies or tax cuts designed to boost economic activity and stimulate growth during or after a recession.

Unemployment Rate

The ratio of workers in the labor force who are unemployed and on the hunt for a job.

Inflationary Pressure

Situations or conditions that lead to an increase in prices across the economy, possibly reducing the purchasing power of money.

Market Interest Rate

The prevailing rate of interest available in the loanable funds market, influenced by supply and demand for credit, central bank policy, and investors’ expectations.