Matrices and transformations questions | form four Basic Mathematics

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#	Question
1	Find the image of the point (2,1) under rotation about the origin through $90^{circ}$ anticlockwise. Mathematical Calculation
2	If $A=egin{pmatrix} 2 &-3 \ 1& -2 end{pmatrix}$ , $B=egin{pmatrix} 3 &4 \ -3& 1 end{pmatrix}$ and $C=egin{pmatrix} 1 &7 \ 2& -3 end{pmatrix}$ , Find the value of 4A-3B+2C. Mathematical Calculation
3	Given that $A=egin{pmatrix} 4 &-3 \ 1& -2 end{pmatrix}$ , $B=egin{pmatrix} 3 &2 \ -4& 0 end{pmatrix}$ and $C=egin{pmatrix} -1 &3 \ 5& -2 end{pmatrix}$ . Find $left \| 3A-2B+C ight \|$ Mathematical Calculation
4	Solve for x and y in $egin{pmatrix} x\3 end{pmatrix} = egin{pmatrix} 2\x+y end{pmatrix}$ . Mathematical Calculation
5	A point (x, y) is rotated through 90° and then reflected about the line y = x. Find: A single matrix for this double transformation. The image of the point (3, 6) under this double transformation. Mathematical Calculation
6	Find the image of a line 5x +10y+ 9 = 0 under a reflection in the line y = x. Mathematical Calculation
7	Find the matrix which enlarges the vector r = (3, 4) to r'= (18, 24) Mathematical Calculation
8	If $M=egin{bmatrix} cos 2alpha & sin 2alpha\ sin 2alpha& -cos 2alpha end{bmatrix}$ , is the matrix of reflection in a line inclined at $ar{alpha}$ , where $alpha$ = 135°, u = ( 6, I) and t=4, Find M(tu). Mathematical Calculation
9	Use inverse matrix method to solve the following system of equations: $left{egin{matrix} 2x+3y=12\ 3x=7+y end{matrix} ight.$ Mathematical Calculation
10	Determine the value of k for which the matrix $egin{pmatrix} k+3 &0 \ 0&2 end{pmatrix}$ has no inverse. Mathematical Calculation