(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a linear system has the augmented matrix:

a, -b, 4, 0

1, -2, 1, 0

0, 0, 4, 0

then select all correct answers:

(a)The system has infinitely many solutions if b=2a;

(b)The system is inconsistent if b=2a;

(c)The system is consistent if b=a;

(d)The system has exactly one solution if a=b=0;

(e)The system has exactly one solution if 2a doesn't equal "b"

2. Relevant equations

None

3. The attempt at a solution

So my prof didn't explain this topic at all, but it's in an assignment that is due on Sunday night...

I've tried my own approach, but somehow I don't get the right answers...

I did matrices separately for the 3 cases: "b=2a", "b=a" and "a=b=0"

Case 1: b=2a

I won`t write out the whole process (because its hideous) but here is the matrix I got in the end:

1, 0, 0, 0

0, 1, -2, 0

0, 0, 4a, 0

So I figured this would mean that the system would have an infinite number of solutions. Thus, if b didn`t equal 2a, then the system should have a unique solution. So I eliminated (b) from the list.

Case 2: b=a

This time I got:

1, 0, 0, 0

0, 1, -2, 0

0, 0, -a, 0

And that would mean that the system has an infinite number of solutions, once again. So (c) holds up as true.

Case 3: a=b=0

1, 0, 0, 0

0, 1, -2, 0

0, 0, 0, 0

Which would once again mean that it has an infinite number of solutions. This would make (d) false

So is my logic right at all? I honestly don`t know what else to do.. Thanks in advance!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Matrix (more or less theoretical)

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