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.
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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,