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.
- فلسطين: الصف ١١
- إيران: الصف ١٢
- أفغانستان: الصف ١١
- فرنسا: الصف ١٢
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
The مقلوب المصفوفة A−١ undoes A: A×A−١ = 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−١.
A system AX = B is solved by X = A−١B. The inverse goes in front. Ask your child to check the answer in the original equations.