Let AX=B be a system of n-linear equations in n-unknowns ( in the usual notation ) such that A is a non singular matrix , then the system is consistent and has a unique solution given by

Theorem 1: If A is a non-singular matrix; then the system of equations given by AX=B has the unique solution given by X=A^(-1)B

The system of equations AX=D has unique solution if

Cramer's rule for system of n linear equations

The system AX = B of n equation in n unknown has infinitely many solutions if

Which of the following system of equations has unique solutions

Let AX = B be a system of n smultaneous linear equations with n unknowns. Statement -1 : If absA=0and (adjA)B ne 0 , the system is consistent with infinitely many solutions. Statement -2 : A (adjA)=absAI

Solution of system of linear equations by matrix method

if the system of equations has a non – trivial solution, then =

A non-Homogeneous system of 3 equations in three unknowns AX=D has no solution, if