lect1111Consistencies

lect1111Consistencies - MATH 17100 28446 11/11/2009...

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

View Full Document Right Arrow Icon
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 aa    , in terms of the equation that row represents, 12 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, 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 x0 will always be a solution to the homogeneous equation, in fact this solution is called the trivial solution .
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

lect1111Consistencies - MATH 17100 28446 11/11/2009...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online