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FP1 Matrices

M= [6 -3] Show that the whole plane is mapped onto 2x+3y=0
[-4 2]

I know that it's mapped onto a straight line because M is singular as detM=0 but how do I find out that the line it maps onto is 2x+3y=0 ?

Thanks :h:
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Avatar for davros
davros
16
Original post by Hoosierette
M= [6 -3] Show that the whole plane is mapped onto 2x+3y=0
[-4 2]

I know that it's mapped onto a straight line because M is singular as detM=0 but how do I find out that the line it maps onto is 2x+3y=0 ?

Thanks :h:


What does a typical vector (a b) (assume I've written it vertically!) map to under this matrix?
Reply 2
Avatar for Smaug123
Smaug123
15
Original post by Hoosierette
M= [6 -3] Show that the whole plane is mapped onto 2x+3y=0
[-4 2]

I know that it's mapped onto a straight line because M is singular as detM=0 but how do I find out that the line it maps onto is 2x+3y=0 ?

Thanks :h:

As davros says, you can consider what a typical vector maps to - if that's too much symbol-shunting, you can do it by working out where the vectors (1,0) goes to. You also have that (0,0) stays the same. Because those points are on the final line, you can then work out what the line actually is.

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