{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lect1111Consistencies

lect1111Consistencies - MATH 17100 28446 Varieties of...

This preview shows pages 1–2. Sign up to view the full content.

MATH 17100 28446 11/11/2009 Varieties of Systems of Linear Equations If in a row-reduced form of an augmented matrix, we encounter a row where all the elements except the last one is 0, i.e. 0 0 0 , 0 0 0 0 0 a a , in terms of the equation that row represents, 1 2 0 0 0 n x x x a , we have a contradictory statement . We say that the system of equations that gave rise to this row-reduced echelon form is inconsistent . In other words, an inconsistent system has no solution. On the other hand, a consistent system has a solution. It may even have more than one solution. If in , Ax b b 0 , we say that the system is a homogeneous system . In a homogeneous system, Ax 0 , the situation that gave rise to inconsistency can never occur since the last column of the augmented matrix of the homogeneous system has all zero elements. Hence a homogeneous system is always consistent. We know that x 0 will always be a solution to the homogeneous equation, in fact this solution is called the

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

lect1111Consistencies - MATH 17100 28446 Varieties of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online