Hello everyone

I am studying linear algebra and these problems came across:

1

Solve all values on a in the equation system

$\displaystyle \left(\begin{array}{cc|c}1&a&1\\a&-1&-1\end{array}\right)$

2

If a ≠ 1 solve the equation system with n equations and $\displaystyle n$ unknown variables.

What happens if $\displaystyle a = 1$?

Ugh, I think i'll just scan this problem and upload it.

3

Solve for all values on a and b in the equation system.

Ok, what can we do?

Problem 1

We need to remove the lower-left a, so we got to multiply the first equation with a.

$\displaystyle \left(\begin{array}{cc|c}1&a&1\\a&-1&-1\end{array}\right)$

$\displaystyle \left(\begin{array}{cc|c}a&a^2&a\\a&-1&-1\end{array}\right)$

Now the a will go away but what happens with the second variable?

$\displaystyle \left(\begin{array}{cc|c}a&a^2&a\\0&???&???\end{ar ray}\right)$

Here's where it stops for me. We haven't really gone into things like this. I guess the result might be this:

Second variable:$\displaystyle -1 - 1a^2 = -2a^2$

Sum:$\displaystyle -1 - a = -(1+a)$

I think I won't toch problem 2 & 3 with a stick before getting a grasp of 1.

Thanks for all replies.