Transformations using Matrices (Edexcel A Level Further Maths: Core Pure): Exam Questions

where  and are non-zero constants.

Given that the matrix  is self-inverse,

(a) determine the value of and the possible values for .

The matrix  represents a linear transformation .

Using the smaller value of  from part (a),

(b) show that the invariant points of the linear transformation  form a line, stating the equation of this line.

where is a positive constant.

The matrix  represents a linear transformation .

The triangle  has vertices at the points with coordinates (1, 2), (3, 2) and (2, 5).

The area of the image of  under the linear transformation  is 15

(a) Determine the value of.

The transformation  consists of a stretch scale factor 3 parallel to the -axis with the -axis invariant followed by a stretch scale factor –2 parallel to the -axis with the -axis invariant. The transformation  is represented by the matrix .

(b) Write down the matrix .

Given that  followed by  is the transformation , which is represented by the matrix ,

(c) find the matrix .

(a) Show that the matrix is non-singular.

The transformation  of the plane is represented by the matrix .

The triangle  is transformed to the triangle  by the transformation .

Given that the area of  is 63 square units,

(b) find the area of

(c) Show that the line  is invariant under the transformation