A tech company is developing a new software product and needs to allocate

its resources efficiently. The company has three types of resources: developers,

designers, and testers. The resource requirements for three different projects

$($A$,$ B$,$ and C$)$ are represented by the following vectors:

Project A: developer, $1$ designer, $1$ tester$)$

Project B: $b=(1,2,2)(1$ developer, $2$ designers, $2$ testers$)$

Project C: $c=(1,2,3)(1$ developer, $2$ designers, $3$ testers$)$

Determine if the set of vectors $\{a,b,c\}$ spans the entire three$-$dimensional re$-$

source space. Explain what this means in the context of the company's resource

allocation.