35. Let A be an n x n matrix, and b and æ be vectors of size n x 1. Which statement below is NOT equivalent to the statement rank A = r < n ? (A) The system Ax = 0 has a nontrivial solution (B) A cannot be row reduced to I, (C) JA| = 0 (D) The system Ae = b has either no solution or an infinite number of solutions for every vector b (E) A is nonsingular (Note: 0 is the n x 1 zero vector.)
35. Let A be an n x n matrix, and b and æ be vectors of size n x 1. Which statement below is NOT equivalent to the statement rank A = r < n ? (A) The system Ax = 0 has a nontrivial solution (B) A cannot be row reduced to I, (C) JA| = 0 (D) The system Ae = b has either no solution or an infinite number of solutions for every vector b (E) A is nonsingular (Note: 0 is the n x 1 zero vector.)
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:35. Let A be an n x n matrix, and b and æ be vectors of size n x 1. Which statement below
is NOT equivalent to the statement
rank A = r < n ?
(A) The system Aæ = 0 has a nontrivial solution
(B) A cannot be row reduced to In
(C) |A| = 0
(D) The system Aæ = b has either no solution or an infinite number of solutions for every
vector b
(E) A is nonsingular
(Note: 0 is the n x 1 zero vector.)
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