Answer to Question #196862 in Algebra for Valerie Khumalo

Question

Consider given the system obtained from the augmented matrix below.

abde|cf 

What is the correct option

1. The system has infinitely many solution if a/c= b/d = e/f

2. The system has exactly one solution whenever af 6= db.

3. The system is inconsistent for af 6= ab.

4. The system has no solution if ae = bd.

5. The system has no solution if ae = bf .

Answer 1

 The correct answer is;

4. The system has no solution if ae = bd.

ae=bd is a unique solution of the given system. Consider a system of linear equations 2x + 5y = 7 and 3x + 2y = 6 ... have been made on the augmented matrix,

Not only that but also, Systems of Linear Equations. Augmented Matrix Notation. Another interesting rewriting is x. (1. 2. ) + y. ( 1. −1. ) = (27. 0. ) . This tells us that ..that the system has no solution if ae=bd