Lecture 2172014.pdf

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MATH 2574H
Jasmine Foo

Lecture 2172014Thursday February 13 2014908 AMLinear Systems and Matrices31 review of solving via eliminationA linear system of m equations in n unknownsax axax b1 111221nn1ax axax b2112222nn2ax axax bm11m22mnnnm eqnsrowsIf there is at least one solution the system is consistentIf no solninconsistentIn matrix form m by n matrixa aax b11121n11a aax b21222n22a aaxbm1m2mn2nbasically you get mxn nx1mx1first matrixcoefficient matrix for the linear systemThe second matrix called a column vectorThe Augmented matrix coefficient matrix with the mx1 matrix as the last additional column on itDef An elementary row operation is an operation on a matrix of one of the following forms1 Swap 2 rows dont have to be adjacent2 Multiply one row by a nonzero constant3 Add a multiple of one row to anotherIf A nad B are both matrices and you can convert A to B using only elementary row operatuions then A and B are called row equivalentDef A matrix E is in echelon form if Every row of E that contains all 0s is below every row that has a nonzero entryIn each row of E taht has a nonzero entry the number of leading zeros is strictly bigger than theof leading zeros in the preceding rowExampleGaussian Elimination CalcIV Page 1
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