1: Systems of Equations

Differential Equations and Linear Algebra · LibreTexts

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    • 1.1: Systems of Equations, Geometry
    • 1.2: Systems of Equations, Algebraic Procedures
      We have taken an in depth look at graphical representations of systems of equations, as well as how to find possible solutions graphically. Our attention now turns to working with systems algebraically.
    • 1.3: Gaussian Elimination
      The work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear system with an augmented matrix. A matrix is simply a rectangular array of numbers. The size or dimension of a matrix is defined as m×n where m is the number of rows and n is the number of columns.
    • 1.4: Uniqueness of the Reduced Row-Echelon Form
      As we have seen in earlier sections, we know that every matrix can be brought into reduced row-echelon form by a sequence of elementary row operations. Here we will prove that the resulting matrix is unique; in other words, the resulting matrix in reduced row-echelon does not depend upon the particular sequence of elementary row operations or the order in which they were performed.
    • 1.5: Rank and Homogeneous Systems
    • 1.6: Exercises

    Thumbnail: A linear system in three variables determines a collection of planes. The intersection point is the solution. (CC BY-SA 4.0; Fred the Oyster via Wikipedia)

    This page titled 1: Systems of Equations was last modified on Mon, 31 Oct 2022 16:39:20 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Ken Kuttler (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform.