7. Indicate whether the statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) If a matrix is reduced to reduced row-echelon form by two different sequences of elementary row operations, the resulting matrices will be different. (b) If a matrix is reduced to row-echelon form by two different sequences of elemen- tary row operations, the resulting matrices might be different. (c) 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. (d) If three lines in the ry-plane are sides of a triangle, then the system of equa- tions formed from their equations has three solutions, one corresponding to each vertex.
7. Indicate whether the statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) If a matrix is reduced to reduced row-echelon form by two different sequences of elementary row operations, the resulting matrices will be different. (b) If a matrix is reduced to row-echelon form by two different sequences of elemen- tary row operations, the resulting matrices might be different. (c) 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. (d) If three lines in the ry-plane are sides of a triangle, then the system of equa- tions formed from their equations has three solutions, one corresponding to each vertex.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. Indicate whether the statement is always true or sometimes false. Justify your answer
by giving a logical argument or a counterexample.
(a) If a matrix is reduced to reduced row-echelon form by two different sequences of
elementary row operations, the resulting matrices will be different.
(b) If a matrix is reduced to row-echelon form by two different sequences of elemen-
tary row operations, the resulting matrices might be different.
(c) 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.
(d) If three lines in the ry-plane are sides of a triangle, then the system of equa-
tions formed from their equations has three solutions, one corresponding to each
vertex.
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