Matrix problem. I don't understand why the answer is option c.

[Sonal7]

I did the following multiplication:

-3 6 by x

1 -2 Y

Now I have two equations = -3x +6y = x'
x -2y=y'

I don't know where to go from here.

 

[Harry_the_cat]

Ok.
x' = -3x + 6y
y' = x - 2y as you said.
Now, can you see that -3x + 6y = -3(x -2y)?
So, x' = -3y'.
Or x' + 3y' = 0
So, every image point lies on the line x + 3y = 0.

The answer is d not c.

 

[Sonal7]

Thats very clear. Thank you very much.