Construct a 3 × 3 matrix A = [aᵢⱼ] with aᵢⱼ = 2i − j. Write its order, the number of its elements and the element a₃₁.

1. 1 · Write what is given and what is to be found. Given: aᵢⱼ = 2i − j for i, j = 1, 2, 3. To find: A, its order, its number of elements and a₃₁.
2. 2 · Write the rule. aᵢⱼ is the element in row i and column j. Put each i and j into the formula.
3. 3 · Row 1 (i = 1). a₁₁ = 2 − 1 = 1, a₁₂ = 2 − 2 = 0, a₁₃ = 2 − 3 = −1.
4. 4 · Row 2 (i = 2). a₂₁ = 4 − 1 = 3, a₂₂ = 4 − 2 = 2, a₂₃ = 4 − 3 = 1.
5. 5 · Row 3 (i = 3). a₃₁ = 6 − 1 = 5, a₃₂ = 6 − 2 = 4, a₃₃ = 6 − 3 = 3.
6. 6 · Check and box the answer. A = [1, 0, −1; 3, 2, 1; 5, 4, 3]. Order 3 × 3, 9 elements, a₃₁ = 5.

Scoring tip: Work row by row and show each aᵢⱼ with its working. A slip is then easy to find, and you still earn method marks.