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Linear Algebra and Differential Equations Lecture 1 ● Linear Algebra: mathematics which emerges from trying to solve linear systems Example #1: Find all x and y such that both xy = 1 and 4x+2y = 8 ● Method 1: substitution ● Method 2: elimination (you know how to do both of these) ● Method 3: graph and see where lines intersect ● Method 4: row reduction (what we’ll be doing) Matrix Notation/Augmented Matrix: find general solution to linear system using matrices Strategy = cleverly combine equations to eliminate variables using the following methods (row operations): ● Scale equation/row by nonzero number (constant) ● Add/subtract one equation/row from another ● Rearrange equations/rows Row operations do not alter solutions to the linear system ● A matrix is in echelon form if it fulfills the following: ○ All nonzero rows are above any zero rows ○ Each nonzero leading entry of a row is to the left of any nonzero leading entries of
