Matrices and transformations questions | form four Basic Mathematics

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#	Question
1	A linear transformation T maps the point (x, y) onto $(x^{1},y^{1})$ where $(x^{1},y^{1})$ = (x + y, -x + 2y). Determine the matrix T of this transformation. Find the determinant and inverse of T. Mathematical Calculation
2	Find the matrix B in the equation AB = C, where $A=egin{pmatrix} 7 &5 \ 4& 3 end{pmatrix}$ and $C=egin{pmatrix} 1 &-1 \ 1& 1 end{pmatrix}$ Mathematical Calculation
3	Given that $A=egin{pmatrix} 0 &2x \ x & 0 end{pmatrix}$ , find the values for X if $left \| x ight \|=-8$ . Mathematical Calculation
4	Given matrices $A=igl(egin{smallmatrix} 3 &5 \ 4 & -2 end{smallmatrix}igr)$ , $B=igl(egin{smallmatrix} 3 &-1 \ -3 & 2 end{smallmatrix}igr)$ and $C=igl(egin{smallmatrix} k &-4\ 3 & -2 end{smallmatrix}igr)$ . Find $A^{2}+2A$ Find t and y such that $B^{2}=tB+yI$ where I is an identity matrix. Find the value of k if the determinant of C is 5. A linear translation Q carried point (x, y ) into (x`,y`) such that x`=5x-3y and y`=-2x+4y Determine the transformation matrix Q. Find Q(3,3) Find the image of the point obtained in part (b)(ii) above under Q. Mathematical Calculation
5	Given the matrices $P=egin{pmatrix} 2 & -3 \ 5 & 4 end{pmatrix}$ and $Q=egin{pmatrix} 9 & 12 \ -15 & 3 end{pmatrix}$ . Find $2P-frac{1}{3}Q$ . If the matrix $egin{pmatrix} 4k & 8\ 2 & 9k end{pmatrix}$ is singular , find the possible values of k. Mathematical Calculation
6	Given the matrices $P=egin{pmatrix} 2 & -3\ 5 & 4 end{pmatrix}$ and $Q=egin{pmatrix} 9 & 12\ -15 & 3 end{pmatrix}$ . Find 2P-¹/₃Q. If the matrix $egin{pmatrix} 4k & 8\ 2 & 9k end{pmatrix}$ is singular , find the possible values of k. Mathematical Calculation
7	Solve the following system of linear equations by using the inverse matrix method: $left{egin{matrix} 2x+3y=7 \ y=frac{1}{2}x & end{matrix} ight.$ Mathematical Calculation
8	By using the transformation matrix $egin{pmatrix} 1 & 0\ 0 & -1 end{pmatrix}$ , find the image of the point A(-2,3). Hence, state the axis in which the point is reflected. Mathematical Calculation
9	Find the point P (x,y) if $egin{pmatrix} 2 & 3\ 4 & -1 end{pmatrix}inom{x}{y}=inom{-23}{-11}$ Mathematical Calculation
10	Find the point P (x,y) if $egin{pmatrix} 2 & 3 4 & -1 end{pmatrix}inom{x}{y}=inom{-23}{-11}$ A translation T maps point P(x,y) in part (a) into (3,2). Find where it takes the point (7,4). Find the image of the point obtained in part (b) under a rotation of 90° followed by another rotation of 180° anticlockwise. Mathematical Calculation