The determinant of a 2 × 2 matrix, singular matrices, the inverse, solving simultaneous equations with matrices, and matrices that represent reflections, rotations and enlargements.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
One matrix can reflect, rotate or enlarge every point of a shape at once — and its inverse can undo it or solve a pair of equations in two lines.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
See the determinant as an area scale factor.
Copy these into your notebook in your own words — that is how they stick.
det (a b; c d) = ad − bc. Identity: det = 1.
det = 0 → no inverse.
A⁻¹ = (1/det) (d −b; −c a). A A⁻¹ = A⁻¹ A = I.
A X = B → X = A⁻¹ B (multiply on the LEFT).
x-axis (1 0; 0 −1); y-axis (−1 0; 0 1); y = x (0 1; 1 0); y = −x (0 −1; −1 0).
90° ACW (0 −1; 1 0); 180° (−1 0; 0 −1); 90° CW (0 1; −1 0); general (cos θ −sin θ; sin θ cos θ).
Centre O, scale factor k: (k 0; 0 k).
First X then R → R X. Area scale factor = |det|.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (17 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [8 marks]
A = 2153.
(a) Calculate the determinant of A. [2]
(b) Write down the inverse matrix A⁻¹. [2]
(c) Hence solve the simultaneous equations 2x + y = 4 and 5x + 3y = 11 using matrices. [4]
Question 2 [9 marks]
The triangle ABC has vertices A(1, 1), B(3, 1) and C(1, 2). A transformation is represented by the matrix R = 0−110.
(a) Find the coordinates of the image of A, B and C under R. [3]
(b) Describe fully the transformation represented by R. [2]
(c) X = 100−1 represents reflection in the x-axis. Find the matrix of the transformation that reflects in the x-axis and then rotates through 90° anticlockwise, and describe the single transformation it represents. [4]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.