MATH 1104 Lecture Notes - Lecture 2: Free Variables And Bound Variables, Augmented Matrix, Elementary Matrix
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Math 1104 - lecture 2 solving system of linear equations. Key definitions and theorems: leading entry: a(cid:374) e(cid:374)tr(cid:455) at the left (cid:373)ost part of the ro(cid:449) that is(cid:374)"t a zero, row-echelon form(ref): a form a matrix has when the following 3 conditions are satisfied: 1. )leading entry is 1 in each row, 2. )the leading entry of a row is to the right of the leading entry of the row above it, 3. ) Rows with all zero elements (if applicable), are placed below all rows with non-zero elements in them. Citation for definition - https://stattrek. com/matrix-algebra/echelon-form. aspx: reduced row-echelon form(rref): a row-echelon form matrix in which the leading entry in each row is the only one that is a non-zero entry in its column. Elementary row operations: a matrix can be reduced to ref (or rref) using specific operations known as elementary row operations. Interchanging rows: ri rj (1 < i, j < n, where i, j and n are integers)
