Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Given an n xn-matriz A over a field K ry column vector b, there is a unique column v lution to Ar=0 is the trivial vector x = 0, iff I (A) #0, the unique solution of Ar= b is

Given an n xn-matriz A over a field K ry column vector b, there is a unique column v lution to Ar=0 is the trivial vector x = 0, iff I (A) #0, the unique solution of Ar= b is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Given an n xn-matrix A over a field K, the following properties hold: (1) For every column vector b, there is a unique column vector z such that Ax = b iff the only solution to Ax = 0 is the trivial vector x = 0, iff det(A) # 0. (2) If det (A) #0, the unique solution of Ax=b is given by the expressions det (A¹,..., A-¹, b, Aj+¹, Ij: ...,A") = det (A¹,..., Ai-¹, Ai, Aj+¹,…, A¹) ¹ known as Cramer's rules. (3) The system of linear equations Ax = 0 has a nonzero solution iff det (A) = 0.
Transcribed Image Text:Given an n xn-matrix A over a field K, the following properties hold: (1) For every column vector b, there is a unique column vector z such that Ax = b iff the only solution to Ax = 0 is the trivial vector x = 0, iff det(A) # 0. (2) If det (A) #0, the unique solution of Ax=b is given by the expressions det (A¹,..., A-¹, b, Aj+¹, Ij: ...,A") = det (A¹,..., Ai-¹, Ai, Aj+¹,…, A¹) ¹ known as Cramer's rules. (3) The system of linear equations Ax = 0 has a nonzero solution iff det (A) = 0.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS