Question

Linear Algebra: Solve the system: 2x - 4y + 2z = -6 and -3x + 6y -z = 9. Can this be solved by substitution or elimination method, or is it necessary to use a matrix?

Answer 1

We have three variable yet we only have two equation

Answer 2

so this means that a matrix is necessary and it can't be solved the other ways?

Answer 3

I don't know if this can even be solved by matrix, unless there is something I don't know about

Answer 4

I know that it can be solved via matrix b/c we just learned these. However, I'm not very comforable with the matrix and is why I tried just solving it algebraically...I kept going in circles without arriving at a solution. I guess I have no choice but to force myself to try the matrix. ughh

Answer 5

You can only find a variable in terms of other variable

Answer 6

yes, that's fine.

Answer 7

I had that issue with my last problem...it was 3x - 6y = -9 , -2x + 4y = 6, and -1/2x + y = 3/2.

Answer 8

Now, you have two variable with three equation; this one is solvable

Answer 9

Disregard the last equation and solve first two equations normally. Once you get value for x and y plug into third equation to see if that checkout(=3/2)

Answer 10

my solution was in terms of variables though.

Answer 11

I got x = -3 + 2a and y = a on this one

Answer 12

I can't seem to solve the 2 equation with 3 unknowns problem 2x - 4y + 2z = -6 and -3x + 6y -z = 9. I will try again and hopefully won't lose myself this time.

Answer 13

You can row reduce as you normally would

Answer 14

You will get:

\[S= \left\{\left(\begin{matrix}-3 \\ 0 \\ 0\end{matrix}\right) + t\left(\begin{matrix}2 \\ 1 \\ 0\end{matrix}\right)\|t \in \mathbb{R}\right\}\]

Answer 15

Err, that sucks,, looks like another l anguage...I guess I'd better go brush up on the matrix stuff. Thanks!

Answer 16

okay, okay, I see why I can't setup the matrix. So I got x = 2y - 3, y = x/2 + 3/2, z = -3x + 6y - 9. This sucks