Questions
 Given that A is and A^{1} is
Find the value of a and b in the expression:
(3 mks)  Solve for the unknowns given that the following is a singular matrix.
 Given that A = and B = and that C = AB, find C^{1}
 B is a matrix and C is the matrix
If A is a 2 x 2 matrix and A x B = C. determine the matrix A.  An object of area 20 cm2 undergoes a transformation given by the matrix followed by find the area of the final image
 Find the matrix B such that AB = I and A = Hence find the point of intersection of the lines 3x + 2y = 10 and 3y – 4 = x.
 Given that P = and Q = find the matrix product of PQ. Hence solve the simultaneous eqution below
2x – 3y = 5
 x + 2y = – 3  Solve for x and y in the following matrix equation using elimination method
 A triangle XYZ , X (1, 1) , Y (2, 4) Z (6 , 9) is reflected in the line X axis followed by a reflection in line X= Y. Find the image of the final image
 Triangle ABC is the image of triangle PQR under a transformation M = where P, Q, R map onto A, B, C respectively.
 Given the points P (5, 1) Q (6, 1) and R(4,  0.5) draw the triangle ABC on the grid provided.
 Triangle ABC in (a) above is to be enlarged by scale factor 2 with centre at (11,  6) to map onto A^{1}B^{1 }and C^{1}. Construct and label triangle A^{1}B^{1 }and C^{1 }on the same grid.
 By construction, find the coordinates of the centre and the angle of rotation which can be used to rotate triangle A^{I}B^{I}C^{I }onto triangle A^{II}B^{II}C^{II} whose coordinates are (3, 2) , (3, 6) and (1, 2) respectively.
 Triangle ABC with an area of 15 cm^{2 }is mapped onto triangle A^{I}B^{I}C^{I }using matrix M = . Find the area of triangle A^{I}B^{I}C^{I}.
 T is a transformation represented by the matrix under T a square whose area is 10cm^{2 }is mapped onto a square of area 110cm^{2}. Find the possible values of X
 Triangle A^{1}B^{1}C^{1 }is the image of ΔABC under a transformation represented by the matrix
M =
If the area of triangle A^{1}B^{1}C^{1 }is 54cm^{2}. Determine the area of triangle ABC  Find the matrix B such that AB = I and A = . Hence find the point of intersection of the lines 3x + 2y = 10 and 3y – 4 = x
Answers

 (x3) – (2x) = 0
x32x = 0
2x + x – 3 = 0
x 3 = 0
x=3 
Determinant = + 65 – 49 = 16 
 20x (3  8)
100 area of 1^{st} image.
100 x (4  3)
700 area of 2^{nd }image 




 Det 2  3 = 5
Area of A^{I}B^{I}C^{I }= 5 x 15
= 75 cm^{2}  A.S.F = 110 = 11
10
5X (X)  6 = 11
5X^{2 }+ 6 = 11
5x^{2 }= 5
X^{2 }= 1
X = ±1  Area of the image = Area of the object x Det.
Det. (∆) = 15 – 18 = 3
54 cm^{2 }= A x 3
54 cm^{2 }= A
3
Area of ∆ ABC = 18 cm^{2} 
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