Basic Matrix Algebra with Algorithms and Applications [electronic resource]

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Bibliographic Details
Online Access: Full Text (via Taylor & Francis)
Main Author: Liebler, Robert A.
Format: Electronic eBook
Language:English
Published: Boca Raton : Chapman and Hall/CRC, 2018.
Series:Chapman Hall/CRC Mathematics Ser.
Subjects:

MARC

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505 0 |a Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Examples; Major results/proofs; 1 Systems of linear equations and their solution; 1.1 Recognizing linear systems and solutions; Given a system of equations and a collection of variables, determine whether the system is linear in the given variables; Given a system of linear equations in n variables, determine whether a given n-tuple is a solution; 1.2 Matrices, equivalence and row operations; Given a system of linear equations with numerical coefficients, write the associated augmented matrix and vice versa. 
505 8 |a Given a matrix and sequence of elementary row operations, apply the row operations to obtain an equivalent matrix1.3 Echelon forms and Gaussian elimination; Given a matrix, decide if it is in reduced row echelon form; Given a matrix, apply elementary row operations to obtain an equivalent matrix in reduced row echelon form; Solve several linear systems with the same coefficient matrix at once; 1.4 Free variables and general solutions. 
505 8 |a Given an RREF augmented matrix, write the general solution of the associated linear system in terms of the variables from nonpivotal columns of the coefficient matrix, or state that there is no solutionGiven a system of linear equations, write an associated augmented matrix, apply elementary row operations to obtain an equivalent RREF matrix and write the general solution; 1.5 The vector form of the general solution; Given a matrix A and a vector x, compute Ax if it exists. Translate between a linear system and the associated matrix equation. 
505 8 |a Compute expressions and verify identities using matrix-vector multiplication and linear combinationsGiven Ax =b, with A in an echelon form, write the general solution as a linear combination of basic solutions and the distinguished solution; 1.6 Geometric vectors and linear functions; Interpret vector arithmetic geometrically. Compute distances and angles in R2 and R3; Transform plots to present linear functions and linear systems geometrically; 1.7 Polynomial interpolation 
505 8 |a Determine the general form of a polynomial function having degree at most n and having m specified functional values, n, m ≤ 32 Matrix number systems; 2.1 Complex numbers; Compute sums, differences, products and quotients in ℂ. Compute the zeros of quadratic polynomials; Interpret complex arithmetic in the geometric representation using both the rectangular and polar forms; 2.2 Matrix multiplication; Given matrices, compute sums, scalar multiples and products as indicated, or decide the indicated expression does not exist 
500 |a Given an adjacency matrix, sketch the associated labeled digraph and vice versa. Use matrix multiplication to compute the number of walks of specified type. 
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