Lunu
Badges: 1
Rep:
?
#1
Report Thread starter 6 years ago
#1
Hi,

I'm really struggling with transformation of matrices. Could someone please show me their working to this particular question?

The matrix A [ 1 1 ] (square 2x2 matrix)
[ 1 -1 ]
Represents a combination of an enlargement and a reflection. Find the scale factor of the enlargement and the equation of the mirror line.

(Previously had worked out that A^2 = [ 2 0 ]
[ 0 2 ]


Any help would be really really appreciated!
0
reply
Lunu
Badges: 1
Rep:
?
#2
Report Thread starter 6 years ago
#2
http://filestore.aqa.org.uk/subjects...W-QP-JAN09.PDF Question 5 if it's not clear.
0
reply
TeeEm
Badges: 19
Rep:
?
#3
Report 6 years ago
#3
this is the plan

A2 implies that 2 applications enlarge the area by SF 4
so one application enlarge the area by SF 2
as the enlargement is uniform the length scale factor is √2
factorize √2 out of the matrix

can you see the rest?
0
reply
Lunu
Badges: 1
Rep:
?
#4
Report Thread starter 6 years ago
#4
(Original post by TeeEm)
this is the plan

A2 implies that 2 applications enlarge the area by SF 4
so one application enlarge the area by SF 2
as the enlargement is uniform the length scale factor is √2
factorize √2 out of the matrix

can you see the rest?
I don't see where the SF 4 comes from :/
And I factorised root 2 out but still couldn't see it

sorry I'm really bad at matrices
0
reply
TeeEm
Badges: 19
Rep:
?
#5
Report 6 years ago
#5
(Original post by Lunu)
I don't see where the SF 4 comes from :/
And I factorised root 2 out but still couldn't see it

sorry I'm really bad at matrices
the determinant of a 2 x 2 matrix gives the area scale factor
(minus implies there is a reflection)


so

1 1
1 -1

has determinant -2 (area enlargement of 2 and reflection)

or

2 0
0 2

has determinant 4 (area enlargement 4)


once you factorize the √2 you get


√2/2 √2/2
√2/2 -√2/2


this is reflection I think about the line y=xtan(2θ) where 2θ = 45

I think somewhere in the formula booklet you get some standard matrices
0
reply
maggiehodgson
Badges: 14
Rep:
?
#6
Report 6 years ago
#6
(Original post by Lunu)
Hi,

I'm really struggling with transformation of matrices. Could someone please show me their working to this particular question?

The matrix A [ 1 1 ] (square 2x2 matrix)
[ 1 -1 ]
Represents a combination of an enlargement and a reflection. Find the scale factor of the enlargement and the equation of the mirror line.

(Previously had worked out that A^2 = [ 2 0 ]
[ 0 2 ]


Any help would be really really appreciated!
This is my method - probably not as mathematical as TeeEm's but see what you think.

If you look in the blue formula book you will see that the matrix looks like it should be a reflection in y = xtan theta.

Now work out what all the numbers would have to be so that cos 2theta = sin 2theta (what is the surd when sin = cos),
Then convert them all to that and then put a factor on the outside that turns them all back to 1.

You now have a scale factor and a theta value that you can work out.

Does that make sense?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

How are you feeling being back in school?

Happy (44)
23.28%
Unhappy (53)
28.04%
Conflicted (92)
48.68%

Watched Threads

View All