Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

So I have the system of equations: $$ \begin{align*} 2a+3b+c-6d&= 1 \\ a-b+c+2d&=0\\ 3a+2b+3c-4d&=-1 \end{align*} $$

I have to prove that this system has no solutions. So, first I prove that all of them are linearly independent, this happens when the determinant is different from zero. I form the matrix $$ \begin{bmatrix} 2 & 3 & 1 \\ 1 & -1 & 1 \\ 3 & 2 & 3 \end{bmatrix} $$ and the determinant is indeed different from zero (It would take long to write it here). The system shouldn't have any solutions, so some of the vectors should be linearly independent as well. Can you form for me, the matrix that proves that they are linearly independent?

share|improve this question
    
So, what was happened to $d$'s and their coefficients? –  B. S. Dec 15 '12 at 8:32
    
What is that ?? –  Engmajor Dec 15 '12 at 8:34
    
You have 3 equations but 4 parameters. Which of them are your unknown variables? –  Kaster Dec 15 '12 at 8:38
    
All of them? Why dont you just form the matrice for me,it is kinda urgent...please. –  Engmajor Dec 15 '12 at 8:40
    
Why is it urgent? Is it an assignment? Or an exam problem? –  Christopher A. Wong Dec 15 '12 at 8:41
show 2 more comments

1 Answer

You will not be able to show that there are no solutions. Check out for example $a=\dfrac{9}{5}$, $b=-\dfrac{1}{5}$, $c=-2$, $d=0$.

I suggest going through the row reduction process.

Remark: If you really want to use a determinant, it can be done, though I don't advise it. But you could bring the $d$ stuff to the right hand side, treating $d$ as a parameter, and see what the determinant of the resulting $3\times 3$ tells you.

share|improve this answer
    
Sorry but this is the question on my textbook :/ –  Engmajor Dec 15 '12 at 8:53
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.