MEI FM Year 1 Page 131 Ex6.1 Q12 (MATRICES!!!!)

Hiya, I've been doing this proof question and I'm honestly stuck:

The plane is transformed using the matrix [a b c d] where ad-bc=0.
Prove that the general point P(x,y) maps to P' on the line cx-ay=0.

I got the equations:
x'=ax+by
y'=cx+dy

But I'm really not sure where to go from there. Any help is greatly appreciated, thanks.

(edited 1 year ago)

Reply 1

mqb2766

Original post by aditi_idk

consider cx' - ay' = ...

Reply 2

aditi_idk

Original post by mqb2766

consider cx' - ay' = ...

i got (bc-ad)y = 0 from that
because we know the determinant is 0, would that be all that is required for the proof? or would i have to go further from there?

Reply 3

mqb2766

Original post by aditi_idk

i got (bc-ad)y = 0 from that
because we know the determinant is 0, would that be all that is required for the proof? or would i have to go further from there?

The point (x',y') lies on the line if it satisfies the equation of the line, so it sounds like youve done it (using the fact that the matrix is singular / det is zero).