euclidean m space linear equations n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Euclidean m -Space & Linear Equations PowerPoint Presentation
Download Presentation
Euclidean m -Space & Linear Equations

Loading in 2 Seconds...

play fullscreen
1 / 10

Euclidean m -Space & Linear Equations - PowerPoint PPT Presentation


  • 127 Views
  • Uploaded on

Euclidean m -Space & Linear Equations. Row Reduction of Linear Systems. Matrix. A matrix is a rectangular array of numbers. This array is enclosed in brackets or parentheses. Each number in a matrix is called and element or entry of that matrix.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Euclidean m -Space & Linear Equations' - emma-blackwell


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
euclidean m space linear equations

Euclidean m-Space & Linear Equations

Row Reduction of Linear Systems

matrix
Matrix

A matrix is a rectangular array of numbers.

This array is enclosed in brackets or parentheses.

Each number in a matrix is called and element or entry of that matrix.

Each horizontal line of numbers in a matrix is called a row.

Each vertical line of numbers in a matrix is called a column.

augmented matrix
Augmented Matrix

Matrix arise from a linear system in standard form by deleting all unknowns operations and equal signs.

A vertical line is drawn along the equal signs to separate the constant column.

When an unknown is missing in an equation, the coefficient zero is inserted in the augmented matrix.

elementary row operations
Elementary Row Operations

Multiply a row by a nonzero scalar.

Interchange the positions of two rows.

Replace a row by the sum of itself and a multiple of another row.

example
Example

x1 + x2 + 2x3 = 8

-x1 - 2x2 + 3x3 = 1

3x1 - 7x2 + 4x3 = 10

row equivalent matrices
Row-Equivalent Matrices

When one matrix can be obtained from another matrix by a finite sequence of row operations, the two matrices are said to be row-equivalent.

The underlying linear systems of two row-equivalent matrices have same solutions.

row reduced echelon form
Row-Reduced Echelon Form

A matrix is in row reduced echelon form if it satisfies the following conditions:

  • The first nonzero entry in each row is a 1, the leading 1.
  • All other entries of a column containing a leading 1 are zeros.
  • In any two rows with some nonzero entries, the leading one of the top row is farther to the left.
  • Rows with all zeros are placed below rows with some nonzero entries.
gauss jordan elimination
Gauss-Jordan Elimination

The process of transforming an augmented matrix to an equivalent row-reduced echelon form is called the Gauss-Jordan Elimination.

row echelon form
Row Echelon Form

A matrix is in row echelon form if it satisfies the following conditions:

  • The leading nonzero entry in each row is a 1.
  • All elements below a leading 1 are zeros.
  • In any two rows with leading 1s, the leading 1 of the top row is farther to the left.
  • Rows with all zeros are placed below rows with some nonzero entries.