Matrix arithmetic and algebra
Specialist Mathematics · Unit 1 — Combinatorics, proof, vectors and matrices · Matrices
Learning objectives (6)
LO-1Calculate the determinant and multiplicative inverse of 2 × 2 matrices, with and without technology. If 𝑨 = [𝑎 𝑏 𝑐 𝑑] then det(𝑨) = 𝑎𝑑 − 𝑏𝑐 𝑨−1 = [𝑎 𝑏 𝑐 𝑑]−1 = 1 det(𝑨) [ 𝑑 −𝑏 −𝑐 𝑎 ], det(𝑨) ≠ 0LO-2Define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and multiplicative inverse.LO-3Model and solve problems that involve matrices of up to dimension 2 × 2, including the solution of systems of linear equations, with and without technology.LO-4Understand the matrix definition and notation.LO-5Use matrix algebra properties, including 𝑨 + 𝑩 = 𝑩 + 𝑨 (commutative law for addition) 𝑨 + 0 = 𝑨 (additive identity) 𝑨 + (−𝑨) = 0 (additive inverse) 𝑨𝑰 = 𝑨 = 𝑰𝑨 (multiplicative identity) 𝑨𝑨−1 = 𝑰 = 𝑨−1𝑨 (multiplicative inverse) 𝑨(𝑩 + 𝑪) = 𝑨𝑩 + 𝑨𝑪 (left distributive law) (𝑩 + 𝑪)𝑨 = 𝑩𝑨 + 𝑪𝑨 (right distributive law)LO-6Use matrix algebra to solve matrix equations that involve matrices of up to dimension 2 × 2, including those of the form 𝑨𝑿 = 𝑩, 𝑿𝑨 = 𝑩 and 𝑨𝑿 + 𝑩𝑿 = 𝑪, with and without technology.
Practise these objectives with instant AI marking
Adaptive questions tied to QCAA mark schemes. Free to start.
Start free practice