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Suppose A € M11x9(R). a) If rank(A) = 8, what is nullity (A)? ) What is the maximum possible value of nullity(A)? c) What is the maximum possible value of rank(A)? What then is the minimum possible value of nullity (A)? 1) Is it possible for the columns of A to be linearly independent? If so, what are the rank SA 2

Suppose A € M11x9(R). a) If rank(A) = 8, what is nullity (A)? ) What is the maximum possible value of nullity(A)? c) What is the maximum possible value of rank(A)? What then is the minimum possible value of nullity (A)? 1) Is it possible for the columns of A to be linearly independent? If so, what are the rank SA 2

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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SOLVE PARTS A, B, C, AND D

2. Suppose A € M11×9(R). (a) If rank(A) = 8, what is nullity(A)? (b) What is the maximum possible value of nullity(A)? (c) What is the maximum possible value of rank(A)? What then is the minimum possible value of nullity (A)? (d) Is it possible for the columns of A to be linearly independent? If so, what are the rank and nullity of A in this case? (e) Is it possible for the columns of A to span R¹¹? If so, what are the rank and nullity of A in this case? (f) What is the minimum possible value of nullity(Aª)? (g) Is it possible for the rows of A to be linearly independent? If so, what are the rank and nullity of A in this case? (h) Is it possible for the rows of A to span Rº? If so, what are the rank and nullity of A in this case?
Transcribed Image Text:2. Suppose A € M11×9(R). (a) If rank(A) = 8, what is nullity(A)? (b) What is the maximum possible value of nullity(A)? (c) What is the maximum possible value of rank(A)? What then is the minimum possible value of nullity (A)? (d) Is it possible for the columns of A to be linearly independent? If so, what are the rank and nullity of A in this case? (e) Is it possible for the columns of A to span R¹¹? If so, what are the rank and nullity of A in this case? (f) What is the minimum possible value of nullity(Aª)? (g) Is it possible for the rows of A to be linearly independent? If so, what are the rank and nullity of A in this case? (h) Is it possible for the rows of A to span Rº? If so, what are the rank and nullity of A in this case?
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