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Let A be a nonzero 3 x 6 matrix. (a) What is the maximum rank that A can have? (b) If rank(A|B) = 2, then for what value of rank(A) is the system Ax = B (with B = 0) inconsistent? For what value of rank(A) is the system Ax = B (with B 0) consistent? (c) If rank(A) = 2, then how many parameters does the solution of the system Ax = 0 have?

Let A be a nonzero 3 x 6 matrix. (a) What is the maximum rank that A can have? (b) If rank(A|B) = 2, then for what value of rank(A) is the system Ax = B (with B = 0) inconsistent? For what value of rank(A) is the system Ax = B (with B 0) consistent? (c) If rank(A) = 2, then how many parameters does the solution of the system Ax = 0 have?

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
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Let A be a nonzero 3 x 6 matrix. (a) What is the maximum rank that A can have? (b) If rank(A|B) = 2, then for what value of rank(A) is the system Ax = B (with B = 0) inconsistent? For what value of rank(A) is the system Ax = B (with B 0) consistent? (c) If rank(A) = 2, then how many parameters does the solution of the system Ax = 0 have?
Transcribed Image Text:Let A be a nonzero 3 x 6 matrix. (a) What is the maximum rank that A can have? (b) If rank(A|B) = 2, then for what value of rank(A) is the system Ax = B (with B = 0) inconsistent? For what value of rank(A) is the system Ax = B (with B 0) consistent? (c) If rank(A) = 2, then how many parameters does the solution of the system Ax = 0 have?
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