Explanation Consider a square matrix A . If the matrix obtained after row reduction has identity matrix on the left side then the matrix obtained on the right is the required inverse of A otherwise A is singular. As the matrix A row-reduces to a matrix with a row of zeros. Thus, the square matrix A cannot be further reduced to obtain the identity matrix. And, if the augmented matrix with n × n matrix A on the left and n × n identity matrix on the right has a row of zeros in the left n × n block, then A is singular. Since, A represents the coefficient matrix of the system of n linear equations, and the system is uniquely determined. In the matrix equation A X = B , the matrix A has entries equal to the coefficients of the left hand side of the system of equations and the matrix X is the column matrix of the unknowns in the system and the matrix B is the column matrix and has entries equal to the coefficients of the right hand side of the system of equations. Consider the equation A X = B . Multiply both sides on the left of the equation by A − 1

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.3, Problem 77E

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The reason why the square matrix A is singular if the matrix A row-reduces to a matrix with a row of zeros.

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Chapter 5.3, Problem 76E

Chapter 5.3, Problem 78E

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Finite Mathematics and Applied Calculus (MindTap Course List)

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The reason why the square matrix A is singular if the matrix A row-reduces to a matrix with a row of zeros.

Solution Summary: The author explains that matrices represent a unique system of linear equations, and if the matrix A has an identity matrix on the left side, it is singular.

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The reason why the square matrix A is singular if the matrix A row-reduces to a matrix with a row of zeros.

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Chapter 5 Solutions