Inverse matrices and solving systems
Find the inverse of a 2 × 2 matrix from its determinant, find a 3 × 3 inverse by row operations, and solve a system with it.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- UK: Year 12
- France: grade 12
- Iran: grade 12
- Afghanistan: grade 11
- Palestine: grade 11
Guide
The inverse matrix A−1 undoes A: A×A−1 = I. It only exists when the determinant is not 0.
For a 2 × 2 matrix with entries a, b, c, d: swap a and d, change the signs of b and c, and divide everything by the determinant ad − bc.
For a bigger matrix, write A next to the identity matrix I and use row operations until the left side is I. What is on the right is A−1.
A system AX = B is solved by X = A−1B. The inverse goes in front. Ask your child to check the answer in the original equations.