Proving Parallel Lines with Matrices: Q3

[BilloRani2012]

Homework Statement

If

l -1 2 l l x l = l 2 l
l 1 -2 l l y l l 1 l

Show that the two lines are parallel and so never cross.

Homework Equations

The Attempt at a Solution

I have attempted it, and so far all i have done is find the determentant. When i do this, i get zero:

det = ad - bc
= (-1*-2) - (2*1) = 0

So, is this all I have to do to prove that the lines are parallel?

 

[ideasrule]

Yes, except you should explain your reasoning. I would explain it as:

If the determinant is 0, the matrix is singular, meaning it doesn't have a unique solution. For a system of two lines in 2D space, this is only possible if they're parallel.

 

[BilloRani2012]

okay thanks :) could be please try and help me with my other question i put up? it's called Matrices Question 2...thanks again