Give an example of each of the following or explain why no such example can exist: (a) An inconsistent linear system in three variables, with a coefficient matrix of rank two. (b) A consistent linear system with three equations and two unknowns, with a coef- ficient matrix of rank one.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Give an example of each of the following or explain why no such example can exist:
(a) An inconsistent linear system in three variables, with a coefficient matrix of rank
two.
(b) A consistent linear system with three equations and two unknowns, with a coef-
ficient matrix of rank one.
Transcribed Image Text:Give an example of each of the following or explain why no such example can exist: (a) An inconsistent linear system in three variables, with a coefficient matrix of rank two. (b) A consistent linear system with three equations and two unknowns, with a coef- ficient matrix of rank one.
Expert Solution
Step 1

The following definitions are used to obtain the required solution.

  • If a system of linear equations has at least one solution, then the system is said to be consistent.
  • If a system of linear equations has no solution, then the system is said to be inconsistent.
  • The rank of a matrix is equal to the order of its largest nonsingular submatrix.
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