1. ## System of equations

This question is under the Matrices topic.
I tried solving using Row Reduction and found that if a=-2, the equations are undefined.

2. Originally Posted by stpmmaths
This question is under the Matrices topic.
I tried solving using Row Reduction and found that if a=-2, the equations are undefined.

After a few row operations on the augmented matrix you get:

$\displaystyle \left[ \begin{array}{ccc|c} a&1&1&1\\ 0&a-1&1-a&a(1-a)\\ 1-a&0&a-1&(a-1)(a+1) \end{array} \right]$

I suggest you now consider the cases $\displaystyle a = 1$ (which corresponds to infinite solutions) and $\displaystyle a \neq 1$. The case $\displaystyle a \neq 1$ might break down into two more cases, if there's another important value of $\displaystyle a$ to consider ....

3. Discuss and find(where possible) the solutions to this system as a takes on all real values.
What does that means?

4. Originally Posted by stpmmaths
What does that means?
If you honestly have no idea, then I'm not sure why you are attempting this question. You need to think about what it means. Go back to your class notes or textbook and review similar examples.

5. The thing is that there is no example relating to this question. I was given this question and was asked to complete it

6. Originally Posted by stpmmaths
The thing is that there is no example relating to this question. I was given this question and was asked to complete it

If you know nothing about the theory behind this type of question then I don't see how you can be guided towards a solution. And I'm not willing to give a complete solution (particularly since it appears you would not even understand it).

Do you know how to solve systems of linear equations using Gaussian elimination? Do you understand the three types of solutions that are possible (unique, infinite, none)? These are the things you will have to review in your class notes and textbook if you are to understand how to do this question.

7. Originally Posted by mr fantastic
If you know nothing about the theory behind this type of question then I don't see how you can be guided towards a solution. And I'm not willing to give a complete solution (particularly since it appears you would not even understand it).

Do you know how to solve systems of linear equations using Gaussian elimination? Do you understand the three types of solutions that are possible (unique, infinite, none)? These are the things you will have to review in your class notes and textbook if you are to understand how to do this question.
I don't want the answer to this question, just want to know what is this question want us to do? Er...I think slowly getting it...

By the way, I do know about Gaussian Elimination, the three types of solutions(infinite- 0=0, unique-number of equations=unknowns and none-Inconsistent).

Besides, I do know Gauss-Jordan method, Augmented matrix, Eigenvalues and Eigenvectors.

8. Originally Posted by mr fantastic
After a few row operations on the augmented matrix you get:

$\displaystyle \left[ \begin{array}{ccc|c} a&1&1&1\\ 0&a-1&1-a&a(1-a)\\ 1-a&0&a-1&(a-1)(a+1) \end{array} \right]$

I suggest you now consider the cases $\displaystyle a = 1$ (which corresponds to infinite solutions) and $\displaystyle a \neq 1$. The case $\displaystyle a \neq 1$ might break down into two more cases, if there's another important value of $\displaystyle a$ to consider ....
$\displaystyle a \neq 1$ break down to two more cases?

And why do it's not in row echelon form?

9. Originally Posted by stpmmaths
I don't want the answer to this question, just want to know what is this question want us to do? And your post is the way to tackle this question?

By the way, I do know about Gaussian Elimination, the three types of solutions(infinite- 0=0, unique-number of equations=unknowns and none-Inconsistent).

Besides, I do know Gauss-Jordan method, Augmented matrix, Eigenvalues and Eigenvectors.
Then read posts #2, #6. Your question requires you to discuss the different possible solutions for al the different values of a. Simple eg. ax + y = 2, x + y = 3. a = 1 => no solution, any other value of a => unique solution.

10. Originally Posted by mr fantastic
Then read posts #2, #6. Your question requires you to discuss the different possible solutions for al the different values of a. Simple eg. ax + y = 2, x + y = 3. a = 1 => no solution, any other value of a => unique solution.
Ooic, finally I get it. Thanks