Elementary Linear Algebra Exam with Answers

Elementary Linear Algebra Exam with Answers ordered n-tuple - Answer-a solution of a system of linear equations with n unknowns can be written as (s₁ , s₂ ... sn) or and ordered n-tuple consistent (linear system) - Answer-has at least one solution (1 or ∞ solutions) (no 2 since its linear) inconsistent: no solution augmented matrix - Answer-includes solutions elementary row operations - Answer-1. multiply an equation by a non-zero constant 2. add/subtract a multiple of another equation to an equation 3. interchange two equations (like when doing the elimination method) Homogenous linear equation - Answer-matrix form is AX=B, B=0, AX=0 a solution is X=0 all other solutions where X≠0 is 'non-trivial' parametric equations - Answer-when the linear systems coincide (∞ sol) so some variables are assigned arbitrary values so the remaining variable(s) can be found in terms of the arbitrary values if the number of equations exceeds the number of unknowns - Answer-the linear system must be consistent row echelon vs reduced row echelon form - Answer-in reduced row echelon, each leading 1 is in a column with 0s only pivot positions - Answer-where the leading 1s are in a row echelon gaussian vs gauss-jordan elimination - Answer-gaussian: gets row echelon form gauss-jordan: gets reduced row echelon form