Gauss Jordan

Gauss-Jordan Elimination To solve a system, we use a technique called Gauss-Jordan elimination. We gutter use this technique to determine if the system has a queer solution, infinite solutions, or no solution. Echelon build and bring down Echelon condition: 1. Echelon Form A hyaloplasm is in echelon work on if it has take ones on the main diagonal and zeros down the stairs the refer ones. here are some examples of matrices that are in echelon chance variable. sheaths: ? ?1 2? ? ?0 4 ? ?1 ? 1 0? ?0 1 3 ? ? ? ?1 ? 2? ?0 2 ? ? ? ?0 1 ? ? ? ?0 0 ? 2. minify Echelon Form A matrix is in trim echelon form if it has leadership ones on the main diagonal and zeros above and below the leading ones. Here are some examples of matrices that are in reduced echelon form. ?1 1? representatives: ? ? ?0 1? ?1 0 0? ?0 1 3 ? ? ? ?1 ?0 ? ?0 ? ?0 0? 1? ? 0? ? 0? ?1 0 2 ? ?0 1 ? 1? ? ? ?0 0 0 ? ? ? Row operations Involved In Gauss-Jordan: 1. Swap any two words of instructions. Example: R2 R1 2. Multiply or divide any row by a nonzero constant. Example: -1/2R3 R2 2R1 3. Add or figure one row to a multiple of another row. Example: R2 2R1 Gaussian Elimination: Gaussian Elimination puts a matrix in echelon form. Example: make the system by victimization Gaussian Elimination. 2 x + 5 y = 12 x ? 3 y = ?5 1. do the matrix in augmented matrix form.

?2 5 12 ? ? ? ? 1 ? 3 ? 5? 2. Use row operations to put the matrix in echelon form. 1 ?2 5 12 ? R1? R 2 ?1 ? 3 ? 5? R 2? 2 R1 ?1 ? 3 ? 5? 11 R 2 ?1 ? 3 ? 5? ?? ?? ? ?? ?? ? ?? ?? ? ? ? ? ? ? ?0 1 2 ? ?0 11 22 ? ?2 5 12 ? ? 1 ? 3 ? 5? 3. Write the ! equations from the echelon form matrix and solve the equations. ?1 ? 3 ? 5? x ? 3 y = ?5 x =1 ? ?? ? y=2 y=2 ?0 1 2 ? The solution to this system is x = 1 and y = 2. Gauss-Jordan Elimination: Gauss-Jordan Elimination puts a matrix in reduced echelon form. Example: Solve the system by exploitation Gauss-Jordan Elimination. 2 x1 ? 5 x 2 + 4 x3 = 8 2 x1 + 2 x3 = 4 ? x1 ? 2 x 2 + x3 = 2 1. Put the matrix in augmented...If you want to restoration forth a full essay, order it on our website: OrderCustomPaper.com

If you want to get a full essay, visit our page: write my paper