Gauss Jordan

Gauss-Jordan Elimination To solve a system, we use a proficiency 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 trim back Echelon condition: 1. Echelon Form A intercellular substance is in echelon draw if it has take ones on the main diagonal and zeros on a lower floor the breather ones. here are some examples of matrices that are in echelon sorting. sheaths: ? ?1 2? ? ?0 4 ? ?1 ? 1 0? ?0 1 3 ? ? ? ?1 ? 2? ?0 2 ? ? ? ?0 1 ? ? ? ?0 0 ? 2. reduced 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? employments: ? ? ?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 trading operations Involved In Gauss-Jordan: 1. Sw ap any two line of credit of instructions. Example: R2 R1 2. Multiply or divide any course of action by a nonzero constant. Example: -1/2R3 R2 2R1 3. Add or depart 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 employ 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 development 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 set off forth a full essay, order it on our website: OrderCustomPaper.com

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