Help with Futher maths please?

I'm doing matrices and I really don't understand how to find the equation of the invariant line?

If anyone know how to do it could you please explain or at least direct me to some place that would explain it.

Thank you x

Reply 1

B_9710

Could you give an example of a matrix and I shall demonstrate it for you.

(edited 8 years ago)

Reply 2

ginga.ninga

Original post by B_9710

Could you give an example of a matrix and I shall demonstrate it for you.

So I have a square which is 2 by 2 and the lower left point is at the point (0,0). Then I had to plot the square which was 4 times the original square.

so that matrices to make it 4 times bigger would be would be
[4, 0 ]
0, 1

The question then asks me for the equation of the invariant line and I just don't get it.

Reply 3

B_9710

Original post by ginga.ninga

The matrix you have given is a stretch parallel to the x axis.
Do you know what an invariant line is?

Reply 4

ginga.ninga

Original post by B_9710

The matrix you have given is a stretch parallel to the x axis.
Do you know what an invariant line is?

No, sorry I don't understand what an invariant line is in the first place?
That's probably where I'm going wrong.

Reply 5

B_9710

Original post by ginga.ninga

No, sorry I don't understand what an invariant line is in the first place?
That's probably where I'm going wrong.

An invariant line is a line whose image under the matrix transformation is the line itself. All this means is that any point on a line will be transformed onto the same line. So if the invariant line of a matrix transformation is say y=2x, any point in the line, say (1,2) will be transformed into the line y=2x, say (10,20).