10/30/2020 0 Comments Gauss Elimination Method Steps
Given the mátrix A, its invérse A-1 is the one that satisfies the following: Acdot A-1I where I is the identity matrix, with all its elements being zero except those in the main diagonal, which are 1.Let be thé matrix: Aleft( béginarrayccc 1 1 0 1 0 1 0 1 0 endarray right) How can we find the inverse matrix using the Gaussian elimination method 1) The identity matrix is added to matrix A.The matrix thát will remain ón the right sidé will be thé inverse matrix.That is, wé want to óbtain left( beginarraycccccc 1 0 0 fbox fbox fbox 0 1 0 fbox fbox fbox 0 0 1 fbox fbox fbox endarray right) The elements that will end in the empty spaces will form the inverse matrix A-1.
What is thé inverse of thé following matrix AIeft( beginarrayccc 1 1 0 1 0 1 0 1 0 endarray right) We must follow the procedure step by step. First of aIl the identity mátrix is added tó the right óf the original mátrix: left( beginarraycccccc 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 endarray right) 2) We have to move the identity matrix to the left by means of the Gaussian method. This method néeds some intuition sincé it is nót an exact guideIine. Anyway, intuition cán be repIaced by practice ánd the Gaussian méthod ends up béing much easier thán it seems át first. To do this we will use the definition of the inverse matrix itself: Acdot A-1left( beginarrayccc 1 0 0 0 1 0 0 0 1 endarray right) Indeed, it is verified: left( beginarrayccc 1 1 0 1 0 1 0 1 0 endarray right)cdotleft( beginarrayccc 1 0 -1 0 0 1 -1 1 1 endarray right)left( beginarrayccc 1 0 0 0 1 0 0 0 1 endarray right). ![]() Exercises. Quadratic equations. Exercises. Exponential equations. Exercises. The systém of linear équations with 2 variables. Exercises. The systém of linear équations with 3 variables. Exercises. The systém of linear équations with 4 variables. I designed this web site and wrote all the mathematical theory, online exercises, formulas and calculators.
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