Linear Algebra a. Show that for every n x m matrix A with rank(A) m, there exists a vector b in R" such that the system Az = b%3Dis inconsistent.

(a) Consider an n×m matrix A. A=a11⋯⋯a1m⋮an1⋯⋯amn

Answered: a. Show that for every n x m matrix A…

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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Linear Algebra

a. Show that for every n x m matrix A with rank(A)<n, there exists a vector b in R" such that the system
b is inconsistent.
Hint: Consider an n x m matrix A. For E
rref( A), show that there exists a vector č in R" such that the
|3D
system Er = e is inconsistent; then, "work backward."
b. Show that for every n x m matrix A with n > m, there exists a vector b in R" such that the system Az = b
%3D
is inconsistent.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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