If A be a 3 X 3 singular matrix of rank 2 and rank(A|B)= 3, (where (A|B) is the augmented matrix), then the system of linear equations Ax=B has
A) Unique solution B) Infinitely many solutions C) No solution
D) At least one but finitely many solutions
Let AX=B be a system of linear equations .
Now here rank of the coefficient matrix A is 2 and that of augmented matrix [A B] is 3
So rank of coefficient matrix is not equal to augmented matrix.
Hence the system of equations is inconsistent
Hence option (C) is correct
Now here rank of the coefficient matrix A is 2 and that of augmented matrix [A B] is 3
So rank of coefficient matrix is not equal to augmented matrix.
Hence the system of equations is inconsistent
Hence option (C) is correct