True or False? In Exercises 59 and 60, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. 59. (a) A 6 × 3 matrix has six rows. (b) Every matrix is row-equivalent to a matrix in row-echelon form. (c) If the row-echelon form of the augmented matrix of a system of linear equations contains the row [1 0 0 0 0], then the original system is inconsistent. (d) A homogeneous system of four linear equations in six variables has infinitely many solutions.
True or False? In Exercises 59 and 60, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. 59. (a) A 6 × 3 matrix has six rows. (b) Every matrix is row-equivalent to a matrix in row-echelon form. (c) If the row-echelon form of the augmented matrix of a system of linear equations contains the row [1 0 0 0 0], then the original system is inconsistent. (d) A homogeneous system of four linear equations in six variables has infinitely many solutions.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.2: Guassian Eliminationa And Guass-jordan Elimination
Problem 59E: True or False? In Exercises 59 and 60, determine whether each statement is true or false. If a...
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True or False? In Exercises 59 and 60, determine
whether each statement is true or false. If a statement
is true, give a reason or cite an appropriate statement
from the text. If a statement is false, provide an example
that shows the statement is not true in all cases or cite an
appropriate statement from the text.
59. (a) A 6 × 3 matrix has six rows.
(b) Every matrix is row-equivalent to a matrix in
row-echelon form.
(c) If the row-echelon form of the augmented matrix
of a system of linear equations contains the row
[1 0 0 0 0], then the original system is inconsistent.
(d) A homogeneous system of four linear equations in
six variables has infinitely many solutions.
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