True or False? Linear Algebra Matrix

[flyingpig]

Homework Statement

The solution set of a linear system involving variables x₁,...,x_n is a lists of numbers (s₁,...,s_n) that makes each equation in the system a true statement when the values s₁,...,s_n are substituted for x₁,...,x_n respectively.

I say it is true because I thought the list meant each solution corresponding the variables is true and so if you plug it in for each one respectively, it should be true.

The Key says it is wrong and it gives a explanation that I don't think it's even English

Solution

False. The description given applied to a single solution. The solution set consists of all possible solutions. Only in special cases does the solution set consist of exactly one solution. Mark a statement True only if the statement is always true.

 

[Ryker]

The solution set of a linear system involving variables x₁,...,x_n is a lists of numbers (s₁,...,s_n) that makes each equation in the system a true statement when the values s₁,...,s_n are substituted for x₁,...,x_n respectively.

I say it is true because I thought the list meant each solution corresponding the variables is true and so if you plug it in for each one respectively, it should be true.

It's false, because it says a list, not, say, all lists of numbers that satisfy the condition.

The Key says it is wrong and it gives a explanation that I don't think it's even English

Solution

False. The description given applied to a single solution. The solution set consists of all possible solutions. Only in special cases does the solution set consist of exactly one solution. Mark a statement True only if the statement is always true.

What's wrong with the explanation? Save for the typo (applies instead of applied) which I don't know if you or the textbook made, it explains perfectly why the answer is "false".

 

[flyingpig]

Probably because I have been working for like three hrs straight.

I don't understand, what is the difference?

all lists of numbers that satisfy the condition. = a lists of numbers (s1,...,sn) that makes each equation in the system a true statement

Is that not the same meaning?

 

[Ryker]

Well, say you have the following system of linear equations:

x₁ + x₂ + x₃ = 0
x₁ + x₂ = 3

Then a "list" of solutions is x₁ = 0, x₂ = 3, x₃ = -3. So if the statement was true, then that list is the solution set to that system of equations. But that is not the only "list" that satisfies the system, as you have infinitely more, for example x₁ = 1, x₂ = 2, x₃ = -3. So the solution set doesn't contain only that first "list", but includes other ones, as well.