Further Mathematics Paper 2, May/June. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength

Question 12

The images of (3,2) and (-1,4) under a linear transformation T and (-1,4) and (7, 11) respectively. P is another transformation where
P: (x, y) - (x + y, x + 2y).
(a) Find the matrices T and P of the linear transformation T and P.
(b) Calculate TP.
(c) Find the image of the point X (4, 3) under TP.

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Observation

The chief examiner stated that most candidates did not attempt this question. Candidates were expected to show that ifT = [~ ~J then [~ ~~] = ~lJ
and (~ ~ J~ 1 J =[;lJ
i.e. 3a + 2b = -1 ............................... (i)
3c + 2d         4 ,,·······""· .. ········(ii)
-a + 4b         7 ......................... (iii)
-c + 4d        11 ........................ (v)
Solving (i) and (iii) simultaneously gave a = -9 and b = 10 . Similarly, solving (ii)         7        7
and (iv) simultaneously gave c = -3 and d = 37 . Thus the transformations are

-9 10J                   7      [_~4 1~ [ J ~1                                     1~
T = !3 ;7 ' P = ~ ~J. Hence TP = !3 ;7i ~ = 11 ;4
7 14                                             ~1         1~              7 14                                                14 7
The image ofx(4,3) under TP = ~ ;4 [~ JWhiCh gave (3;, 1~4).
14         7