Question

Is the statement​ "The solution set of a linear system involving variables x 1 comma ... comma x Subscript n is a list of numbers (s 1 comma ... comma s Subscript n Baseline )that makes each equation in the system a true statement when the values s 1 comma ... comma s Subscript n are substituted for x 1 comma ... comma x Subscript n Baseline comma ​respectively" true or​ false? Explain. A. ​True, because the list of variables (x 1 comma ... comma x Subscript n Baseline )and the list of numbers (s 1 comma ... comma s Subscript n Baseline )have a​ one-to-one correspondence. B. ​False, because the description applies to a single solution. The solution set consists of all possible solutions.

Answer 1

Answer:

  B. ​False, because the description applies to a single solution. The solution set consists of all possible solutions.

Step-by-step explanation:

The choice of true or false revolves around whether a linear system can have more than one solution.

The problem statement does not say the equations are independent, a condition that must be satisfied if there is to be only one solution. Hence we must assume that the system may be dependent or even inconsistent, leading to zero, one, or an infinite number of solutions. The answer above carries its own explanation.

  False, for the reason given