Notes 2 Elementary Row Operations 2010

Notes 2 Elementary Row Operations 2010 - File: Notes 2...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 File: Notes 2 Elementary Row Operations 2009.doc Elementary Row Operations (ERO) An elementary row operation on a matrix A is one of the following operations ( i A represents row i of matrix A ): (i) Row i is interchanged with row j : ji AA ←⎯→ (ii) Row i is multiplied by a nonzero scalar k : ii kA A (iii) Row i is replaced by k times row j + row i : i kA A A + . Elementary row operations are equivalent to pre-multiplying A by some matrix B . For example, B is obtained from an identity matrix with the following three variations for the ERO’s: (i): row (i) of B is T j e and row (j) of B is T i e ; (ii): row (i) of B is T i ke ; (iii): row (i) of B is TT e + . The solution to a system of m equations in n unknowns, Ax b = , is invariant with respect to a finite number of ERO’s. That is ˆ x solves A xb = if and only if ˆ x solves Ax b = , where ( ) , Ab can be obtained from ( ) , by a finite number of ERO’s. Thus, there exists a matrix M such that . b MAx Mb = = = For example, consider the matrix 21 1 121 11 2 A =− . To use (i) such as interchanging rows 1 and 3, M would be
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 001 1 12 0 1 0 and = 1 2 1 100 2 1 1 MM A ⎡⎤ ⎢⎥
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

Notes 2 Elementary Row Operations 2010 - File: Notes 2...

This preview shows document pages 1 - 3. Sign up to view the full document.

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