Matrices and transformations questions | form four Basic Mathematics

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#	Question
1	(a) Given a triangle with vertices A(0, 0) , B(3, 0) and C(3, 1) Í¾ find its image under: (i) a translation by the vector (2, 3) , (ii) the enlargement matrix $egin{pmatrix} 2 & 0 0 & 2 end{pmatrix}$ (b) Sketch the triangle and the images in parts (a)(i) and (ii) on the same pair of axes and comment on their sizes. Mathematical Calculation
2	(a) Given matrices $Q=egin{pmatrix} -3 &1 \ 0 & 2 end{pmatrix}$ and $P=egin{pmatrix} a &b \ c & d end{pmatrix}$ such that $QP=egin{pmatrix} -2 &-2 \ 2 & 2 end{pmatrix}$ , find the elements of matrix P . (b) Determine the matrix A from the equation $egin{pmatrix} 5 &3 \ 4 & 5 end{pmatrix}-2A =egin{pmatrix} -2 &1 \ 3& 5 end{pmatrix}$ Mathematical Calculation
3	Find the inverse of matrix $A=egin{pmatrix} 2 &-3 \ 1&2 end{pmatrix}$ Find the point $P(x,y)$ , If $egin{pmatrix} 2 &-3 \ 1& 2 end{pmatrix} egin{pmatrix} x\y end{pmatrix}=egin{pmatrix} -5\8 end{pmatrix}$ Determine the image of the point obtained in part (2) under enlargement by the matrix $egin{pmatrix} 2 &0 \ 0& 2 end{pmatrix}$ followed by a reflection in the line y= x . Mathematical Calculation
4	Determine a matrix M which represents a reflection in the line y − x = 0 Find the image of the line x + 2y − 4 = 0 after a reflection in the line y − x = 0 . Mathematical Calculation
5	If $A=egin{pmatrix} 3 &2 \ 4&-1 end{pmatrix}$ find $left \|A ight \|$ and $A^{-1}$ . Use the inverse matrix obtained in (1)to solve 3x + 2y = 12 and 4x − y = 5 . Mathematical Calculation
6	Given $A=egin{pmatrix} 2 &6 \ 4 & 8 end{pmatrix}$ find $A^{-1}$ Use the results obtained in part (1) to find the point of intersection of the following system of simultaneous equations: $left{egin{matrix} 2x + 6y = 22\ 4x + 8y = 32\ end{matrix} ight.$ Find the image of the point obtained in part (2) above under a rotation 90° anticlockwise Mathematical Calculation
7	Find the value of k such that the matrix $egin{pmatrix} 2k+2 & k\ 4k-3 & k+3 end{pmatrix}$ is singular. Mathematical Calculation
8	The vertices of ABC are A(1, 2) , B(3, 1) and C(− 2, 1) . If triangle ABC is reflected on the x axis, find the coordinates of the vertices of its image. Mathematical Calculation
9	Solve the following simultaneous equations by matrix method. $left{egin{matrix} 2x+3y-2=0 \ -9y+8x-1=0 end{matrix} ight.$ Mathematical Calculation
10	Reflect the point (1, 2) in the line x + y = 0 . Mathematical Calculation