This question is under the Matrices topic.
I tried solving using Row Reduction and found that if a=-2, the equations are undefined.
Actually I don't know what the question is asking about
This question is under the Matrices topic.
I tried solving using Row Reduction and found that if a=-2, the equations are undefined.
Actually I don't know what the question is asking about
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 ....
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.