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Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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When finding the determinant using cofactor expansion, it is necessary to select the row or column with the greatest number of zeros or ones. If a matrix is augmented, then any row operation performed to the augmented matrix must exclude the entries augmented to the original one. If a square matrix n x n is multiplied to an n x m matrix, where m #n, then the resulting matrix is always singular, and will always have a determinant equal to 0. If a complex number z is situated along the real axis, then the complex conjugate is always - Re(z). D.A system of linear equations with a 0 determinant on its original matrix (i.e., coefficients of the unknowns) will yield to no solution for the values of the unknowns.
Transcribed Image Text:When finding the determinant using cofactor expansion, it is necessary to select the row or column with the greatest number of zeros or ones. If a matrix is augmented, then any row operation performed to the augmented matrix must exclude the entries augmented to the original one. If a square matrix n x n is multiplied to an n x m matrix, where m #n, then the resulting matrix is always singular, and will always have a determinant equal to 0. If a complex number z is situated along the real axis, then the complex conjugate is always - Re(z). D.A system of linear equations with a 0 determinant on its original matrix (i.e., coefficients of the unknowns) will yield to no solution for the values of the unknowns.
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