Linear algebra: mathematics which emerges from trying to solve linear systems. Find all x and y such that both x-y = -1 and 4x+2y = 8. 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): Row operations do not alter solutions to the linear system. A matrix is in echelon form if it fulfills the following: All non-zero rows are above any zero rows. Each non-zero leading entry of a row is to the left of any non-zero leading entries of lower rows. A matrix is in reduced echelon form if it satisfies the above conditions, and also: Non-zero leading entries of rows are 1. There are zeros above a leading non-zero entry.
