Hi, um i just failed my linear exam so but I'm going to take a supplementary exam in a few days so i was wondering if someone could please help me. Because my lecturer is on holiday as its uni holidays now.

Well this is a leontif input-output question. This question comes from my lecture notes, where the model leads to the linear system,

$\displaystyle

\frac{1}{2}x_1 - \frac{3}{5}x_2 - \frac{1}{5}x_3 = 50 $

$\displaystyle

-\frac{1}{5}x_1 + \frac{4}{5}x_2 - \frac{1}{10}x_3 = 30 $

$\displaystyle

-\frac{1}{10}x_1 - \frac{1}{5}x_2 + \frac{7}{10}x_3 = 20 $

and it says that the answer is(to the nearest decimal point):

$\displaystyle

x_1 = 226, x_2 = 119, x_3 = 78 $

But when i did it i got a totally different answer and then decided to check the online calculator:

Linear Algebra Toolkit

yeahhh and it sorta got close to what i got

it says the answer is(to the nearest decimal point):

$\displaystyle

x_1 = 290, x_2 = 123, x_3 = 105 $

I'm just wondering if someone could tell me if my lecture notes are wrong? as i have no idea if they're correct or not. Coz i thought that for leontif input output, all you have to do is get it into reduced row echelon form?

Thank you