Matrices and transformations questions | form four Basic Mathematics

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#	Question
1	Find the enlargement matrix which maps the point (− 3, 4) into (18,− 24) . Mathematical Calculation
2	It is given that $A=egin{pmatrix} 2 &4 \ 3& 1 end{pmatrix}$ , $I=egin{pmatrix} 1 &0 \ 0& 1 end{pmatrix}$ and k is a real number. Find the matrix $A-kI$ Show that the matrix above has no inverse if $k^2 -3k-10=0$ . Mathematical Calculation
3	A transformation T has the matrix $T=egin{bmatrix} 1 &x \ r&-2 end{bmatrix}$ . Under the same transformation T, the point (-4,1) is mapped onto point (6,3). Find x and r. Mathematical Calculation
4	For what values of $n$ will the matrix $egin{pmatrix} n-1 &n+3 \ 1& 6n end{pmatrix}$ be non-singular? Mathematical Calculation
5	If $A=egin{pmatrix} 1 &2 \ 1& 1 end{pmatrix}$ ; $B=egin{pmatrix} 3 &2 \ 4& 5 end{pmatrix}$ .Find $A+B$ $A imes B$ The inverse of $B$ Using the inverse of $B$ in (3) above find the solution of the simultaneous equations $left{egin{matrix} 3x+2y=12\ 4x+5y=23 end{matrix} ight.$ Mathematical Calculation
6	R is a point (1,2). It is translated onto the point S by the vector $egin{pmatrix} 3\ -4 end{pmatrix}$ . Write down , The coordinates of S The vectors that translate S onto R Mathematical Calculation
7	The matrix $egin{pmatrix} -1 &0 \ 0& 1 end{pmatrix}$ represents a single transformation, Describe fully this transformation Find the coordinates of the image at point (5,3) after this transformation. Mathematical Calculation
8	If $M_2$ denotes a reflection in the y-axis and $R_{180}$ a rotation about the origin through an angle of 180 for any point (x,y). Find $R_{180}M_2(x,y)$ and $M_2R_{180}(x,y)$ . Is $R_{180}M_2$ commutative ? give a reason. Mathematical Calculation
9	Given that $A=egin{pmatrix} 1 &2 \ -1& 4 end{pmatrix}$ . Find $A^{2}+5A+6I$ where I is the identity matrix. Mathematical Calculation
10	A linear transfomation T has matrix $egin{pmatrix} 2 &-1 \ 1& 1 end{pmatrix}$ . Find The image of point (2,3) undert T. Coordinates of the point having an image of (7,2) under T by using matrix method. Mathematical Calculation