Final answer:
To ascertain if b is a linear combination of a₁, a₂, and a₃, set up and solve an equation of the form b = k₁a₁ + k₂a₂ + k₃a₃. If a solution for the constants exists, b is a linear combination; otherwise, it's not.
Step-by-step explanation:
To determine if b is a linear combination of vectors a₁, a₂, and a₃, we need to express b as a sum of multiples of a₁, a₂, and a₃. Mathematically, we'd set up an equation of the form b = k₁a₁ + k₂a₂ + k₃a₃, where k₁, k₂, and k₃ are constants to be determined. To establish if such a combination is possible, the equation needs to be solved for these constants. If a solution exists, b is indeed a linear combination of the vectors; if not, it is not a linear combination.