# Given vectors, constructing a matrix

1. Aug 3, 2015

### JesseJC

1. The problem statement, all variables and given/known data
Say you've been given vectors v1, v2 and v3.

2. Relevant equations

3. The attempt at a solution
How do I construct a matrix out of these three vectors? Am I to use the given vectors as columns or rows in a matrix? When does this matter and when does it not? This may be a stupid question, but I haven't been able to find a clear answer. My textbook constructs matrices in both ways, but I'm never clear as to why they construct them as columns or rows. Does it depend entirely on the context and goal of the question? If there's a clear answer for this, I'd appreciate it, thanks.

2. Aug 3, 2015

### RUber

It depends on the context.
I normally like them stacked in rows of I am treating them like a system.
The main thing is to keep track of your given information and make logical steps to your goal.

3. Aug 3, 2015

### JesseJC

So, during an exam you can ruin a question if you incorrectly set the vectors up, right?

4. Aug 4, 2015

### tommyxu3

Maybe it would be, for you may disorder what operations you are doing.
But just like it's mentioned above, you just have to think clearly and make logical steps toward your goal.

5. Aug 5, 2015

### RUber

Do you have a particular application in mind? Have you recently had trouble with this?
Essentially, you are dealing with either one matrix or its transpose. In your notation, you can easily fix any mistakes by adding the ^T to your matrix.

Some applications, like the determinant (if your matrix is square), are the same either way, $|A| = | A^T|$.
Others, like Ax = B, might have entirely different solutions.