MTH 222 Lecture Notes - Lecture 2: Gaussian Elimination, Euclidean Vector, Row And Column Vectors
6 Sep 2016
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If there a contradiction, there is no solution. If each variable is a leading variable in some row, then there is a unique solution. If there exists a variable which is not a leading variable in some row, there is infinitely many solutions. We want to express the solution in terms of constants and free variables. Free variables are variables that do not lead. mult r1 by 3 -x-y+3z=6. Solve r2 for y and substitute into r1 y = 4z-6 since x=-z+3 and y=4z-6, the solution set can be described by (-z+3,4z-6,z) x=4z-6+3z-3 x=-y+3z-3 x=-z+3. Solve for y w = 3, z = 2, y = y. When you solve for x, x = y+1 the solution set is described as {(y+1,y,2,3) for all real numbers y} Definition: an mxn matrix a is a rectangular array of numbers with m rows and n columns. We write a = where ai,j is the entry in the ith row and jth column.
