FP1 Matrix question help :s

1.

The transformation S is a shear with the y-axis invariant (i.e. a shear parallel to the y-axis). It is given
that the image of the point (1, 1) is the point (1, 0)[font="Times"].

Find S

I don't know what to do for this, any help would be really appreciated.

Reply 1

B.Lakeland

2

Original post by AG Singh

1.

The transformation S is a shear with the y-axis invariant (i.e. a shear parallel to the y-axis). It is given
that the image of the point (1, 1) is the point (1, 0)[font="Times"].

Find S

I don't know what to do for this, any help would be really appreciated.

I don't do your exam board or (as it appears syllabus), but from what I can tell, a shear with a y-axis invariant is a matrix of the form {{1,0},{k,1}} where k is a constant.
To find k, I would pre-multiply (1,1) by S to get (1, k+1). This, as we are told in the question, is equal to (1,0). Therefore k+1=0 so k=-1.

As I have said, I do Edexcel, and this is not on our syllabus so I would still get someone else to check

Reply 2

AG Singh

OP

3

Original post by B.Lakeland

I don't do your exam board or (as it appears syllabus), but from what I can tell, a shear with a y-axis invariant is a matrix of the form {{1,0},{k,1}} where k is a constant.
To find k, I would pre-multiply (1,1) by S to get (1, k+1). This, as we are told in the question, is equal to (1,0). Therefore k+1=0 so k=-1.

As I have said, I do Edexcel, and this is not on our syllabus so I would still get someone else to check