Matrices and Line Intersection

I am having difficulty rewriting my function. want to write a function that determines whether or not 2 lines intersect. I know I have to use the backslash to solve for the intersection of 2 equations, but I don't really know where to go from there so I tried my best.

The equations of the lines are :

ax + by = c

px + qy = r

• The inputs, a, b, c, p, q, and r correspond to the coefficients of the equations above. The outputs, xc, yc, flag will be determined as follows:
• If an intersection point exists, the value of flag is 1 and LineIntersect returns the intersection points: xc and yc.

*

• If many intersection points exist, the value of flag is 2, and LineIntersect returns xc and yc as an empty vector.

*

• If no intersection point exists, the value of flag is 3, and LineIntersect returns xc and yc as an empty vector.

This is the code I tried to write. Sorry for the many errors, I tried my best.

function [xc yc flag] = LineIntersect(a,b,c,p,q,r)
a.*x + b.*y = c 
p.*x + q.*y = r
if x*c/y*c
    flag=1
    disp ('xc' 'yc')
elseif x*c/y*c
    flag=2
    ('xc' 'yc')
elseif x*c/y*c
    flag=3
    disp('xc' 'yc')
flag= yc ./xc
end

Here test cases if it makes understanding the problem easier:

href="http://s1308.photobucket.com/albums/s617/pingchu93/?action=view&current=Problem2TestCases_zpse6318f5e.jpg" target="_blank" rel="nofollow noopener noreferrer"<img src="http://i1308.photobucket.com/albums/s617/pingchu93/Problem2TestCases_zpse6318f5e.jpg" border="0" alt="Problem 2 Test Cases"></a>

thanks.

Answer 1

[Matt J]

Hints:

Consider the quantity

 rank([a b c; p q r]) - rank([a b; p q])

What does it tell you if it is greater than 0? Also, what does it tell you if rank([a b ; p q])<2 ?