Matrices — O/L Mathematics

What must I remember about Matrices?

• A matrix is a rectangular array of numbers arranged in rows and columns; the order (dimension) is written m × n (m rows by n columns).
• Matrix equality: Two matrices are equal if and only if they possess identical orders and their corresponding elements are equal.
• Matrix addition and subtraction: Defined ONLY for matrices of identical order; add or subtract corresponding entries: [A + B]ᵢⱼ = aᵢⱼ + bᵢⱼ.
• Scalar multiplication: Multiplying matrix A by scalar k multiplies EVERY element of A by k: k[aᵢⱼ] = [k aᵢⱼ].
• Matrix multiplication: Product AB is defined ONLY if columns of A equal rows of B (order (m × k) × (k × n) ⟹ (m × n)); multiply rows by columns.

Test yourself (1 minute)

1. Order compatibility for operations

   For addition/subtraction, orders must be EXACTLY identical; for multiplication (A × B), inner dimensions must match: (2 × 3) can multiply (3 × 2), but (2 × 3) CANNOT multiply (2 × 3).

2. Matrix multiplication is non-commutative

   In general, AB ≠ BA; never assume matrix products can be reversed.

3. Row-by-column multiplication arithmetic

   Entry c₁₁ is (row 1 of A) dot (col 1 of B): a₁₁b₁₁ + a₁₂b₂₁; take extreme care with negative signs.

Practise Matrices questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 19)

What should I study first?

What comes next?

Next in the syllabus

Where does Matrices fit in the syllabus?

Grade 11 · Term 3