MAT016 · Matrices & determinants · Classes 11–12
Systems using matrices
A system of linear equations can be written AX = B. If det A ≠ 0, the unique solution is X = A⁻¹B, where the two lines cross.
AX = BSystems using matrices
📐 Formula
[a b; c d][x; y] = [e; f] ⇒ X = A⁻¹B
✏️ Worked example
2x + y = 5 and x − y = 1: x = 2, y = 1.
🌍 Where it is used
Mixtures, prices, circuits and economics.
❓ Quick check
If det A = 0, the system has…
🏋️ Practice
EasySolve x + y = 4, x − y = 2.
Answer: x = 3, y = 1
MediumWrite 3x + 2y = 7, x − y = 4 as AX = B.
Answer: [3 2; 1 −1][x; y] = [7; 4]
ChallengeSolve 2x + 3y = 8, x + y = 3.
Answer: x = 1, y = 2