Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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True False b d g i  only 
 
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True-False Exercises TF. In parts (a)-(i) determine whether the statement is true or false, and justify your answer. a. If a matrix is in reduced row echelon form, then it is also in row echelon form. b. If an elementary row operation is applied to a matrix that is in row echelon form, the resulting matrix will still be in row echelon form. c. Every matrix has a unique row echelon form. d. A homogeneous linear system in n unknowns whose cor- responding augmented matrix has a reduced row echelon form with r leading 1's has n - r free variables. e. All leading 1's in a matrix in row echelon form must occur in different columns. f. If every column of a matrix in row echelon form has a leading 1, then all entries that are not leading 1's are zero. g. If a homogeneous linear system of n equations in n unknowns has a corresponding augmented matrix with a reduced row echelon form containing n leading 1's, then the linear system has only the trivial solution. h. If the reduced row echelon form of the augmented matrix for a linear system has a row of zeros, then the system must have infinitely many solutions. i. If a linear system has more unknowns than equations, then it must have infinitely many solutions.
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Transcribed Image Text:True-False Exercises TF. In parts (a)-(i) determine whether the statement is true or false, and justify your answer. a. If a matrix is in reduced row echelon form, then it is also in row echelon form. b. If an elementary row operation is applied to a matrix that is in row echelon form, the resulting matrix will still be in row echelon form. c. Every matrix has a unique row echelon form. d. A homogeneous linear system in n unknowns whose cor- responding augmented matrix has a reduced row echelon form with r leading 1's has n - r free variables. e. All leading 1's in a matrix in row echelon form must occur in different columns. f. If every column of a matrix in row echelon form has a leading 1, then all entries that are not leading 1's are zero. g. If a homogeneous linear system of n equations in n unknowns has a corresponding augmented matrix with a reduced row echelon form containing n leading 1's, then the linear system has only the trivial solution. h. If the reduced row echelon form of the augmented matrix for a linear system has a row of zeros, then the system must have infinitely many solutions. i. If a linear system has more unknowns than equations, then it must have infinitely many solutions.
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