A system of linear equations is represented ...

CBSE Class 12 Math 2025 All Sets Solved Paper

Question : 11 of 20

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A system of linear equations is represented as AX = B, where A is coefficient matrix, X is variable matrix and B is the constant matrix. Then the system of equations is

Consistent, if | A | ≠ 0, solution is given by $X=B A^{-1}$
Inconsistent if | A | = 0 and $(\operatorname{adj} A) B=0$
Inconsistent if | A | ≠ 0
May or may not be consistent if | A | = 0 and $(\operatorname{adj} A) B=0$

Solution:

System of linear equations is represented as Ax = B

If | A | ≠ 0, then system of equations is consistent and solution is given by

X=A^{-1} B.

For inconsistent. | A | = 0 and

(\operatorname{adj} A) B \neq 0

If | A | = 0 and

(\operatorname{adj} A) B=0,

then system may or may not consistent.

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