|Class 12 Maths Determinants||Applications|
Applications of Determinants and Matrices
Case1 : A is a nonsingular
AX = B or X = A–1 B
Case 2 : A is a singular matrix
If A is a singular matrix, then |A| = 0. AX = B or X = A–1 B or X = (1/ |A|) * (adj A) *B
In this case, we calculate (adj A) B.
Numerical: Examine Consistency x + 2y = 2 & 2x + 3y = 3
|A| = -1 ≠ 0, so A-1 exist. Thus it is consistent.