Class 12 Maths Determinants Applications

Applications of Determinants and Matrices

  • Solving the system of linear equations
  • Checking the consistency of the system of linear equations.



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.

  • If (adj A) B ≠ O, then solution does not exist and the system of equations is called inconsistent.
  • If (adj A) B = O, then system may be either consistent or inconsistent according as the system have either infinitely many solutions or no solution


Numerical: Examine Consistency x + 2y = 2 & 2x + 3y = 3


|A| = -1 ≠ 0, so A-1 exist. Thus it is consistent.


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