1 - Pivot

1 - Pivot - Math 1b Practical Basic matrices and solutions;...

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

View Full Document Right Arrow Icon
Math 1b Practical — Basic matrices and solutions; pivot operations January 3, 2011 We use matrices to model systems of linear equations. For example, the system 2 x 1 3 x 2 5 x 3 7 x 4 +2 x 5 =7 x 1 + x 2 5 x 3 + x 4 4 x 5 =3 x 1 4 x 3 +3 x 4 + x 5 = 4 (1) has corresponding matrix 2 3 5 72 11 51 4 10 43 1 7 3 4 . (2) Two matrices (of the same dimensions) are row-equivalent when one can be obtained from the other by a sequence of elementary row operations as described in LADW, Sec- tion 2.1 on page 40. It is important to understand that the systems of linear equations corresponding to two row equivalent matrices will have exactly the same set of solutions. An r by n matrix M with all nonzero rows is basic when its columns include the unit vectors 1 0 0 . . . 0 , 0 1 0 . . . 0 , 0 0 1 . . . 0 , ..., 0 0 0 . . . 1 (of height r )( 3 ) in some order. These may be called the special columns of M . A matrix with some rows of all zeros is called basic when the rows of all zeros are at the bottom and the submatrix consisting of the nonzero rows is basic. All matrices in reduced echelon form are basic matrices. Other examples of e.g. 3 × 7 basic matrices are 2304105 6718009 5505015 , 2174105 6088419 0000000 , 2104100 6018001 5007010 .
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.

This note was uploaded on 11/10/2011 for the course MA 1B taught by Professor Aschbacher during the Winter '08 term at Caltech.

Page1 / 4

1 - Pivot - Math 1b Practical Basic matrices and solutions;...

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