Is the statement The solution set of a linear system involving variables x1, …, xn is a list of numbers (s1, …, sn) that makes each equation in the system a true statement when the values s1, …, sn are substituted for x1, …, xn, respectively true or false? Explain.
False, because the description applies to a single solution. The solution set consists of all possible solutions.
The statement The solution set of a linear system involving variables x1, …, xn is a list of numbers (s1, …, sn) that makes each equation in the system a true statement when the values s1, …, sn are substituted for x1, …, xn, respectively is true.
A linear system involving variables x1, …, xn is a set of linear equations that need to be solved simultaneously to find the values of x1, …, xn that satisfy all the equations in the system. The solution set of a linear system is the set of all possible values of x1, …, xn that make all the equations in the system true.
When we substitute the values of s1, …, sn in place of x1, …, xn respectively, we get a list of numbers (s1, …, sn) that satisfies all the equations in the system and makes them true. Therefore, the statement is true.
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