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12: More Matrix Algebra

  • Page ID
    80481
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    augmented matrix

    There's a Gaussian technique whose intent
    Is to solve the constraints you present
    As a matrix equation—
    Once you've had the occasion
    To write down your constants (augment)

    Steve Ngai, The Omnificent English Dictionary in Limerick Form

     

    In Chapter 5 we studied matrix operations and the algebra of sets and logic. We also made note of the strong resemblance of matrix algebra to elementary algebra. The reader should briefly review this material. In this chapter we shall look at a powerful matrix tool in the applied sciences, namely a technique for solving systems of linear equations. We will then use this process for determining the inverse of \(n\times n\) matrices, \(n\geq 2\), when they exist. We proceed with a development of the diagonalization process, with a discussion of several of its applications. Finally, we discuss the solution of linear equations over the integers modulo \(2\).


    This page titled 12: More Matrix Algebra is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Al Doerr & Ken Levasseur.

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