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Exercise 3.4. Consider the matrix A = -1 3 2 2 -2 6 4 -2 (a) Give a general expression for all vectors in the range of A. What is the rank of A? (b) Using part (a), give a nonzero vector b for which Ax b is compatible. = (c) Give a vector b such that Ax b is not compatible, and explain how you found b.

Exercise 3.4. Consider the matrix A = -1 3 2 2 -2 6 4 -2 (a) Give a general expression for all vectors in the range of A. What is the rank of A? (b) Using part (a), give a nonzero vector b for which Ax b is compatible. = (c) Give a vector b such that Ax b is not compatible, and explain how you found b.

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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Exercise 3.4. Consider the matrix A - 3 2 -2 6 4 1 -1 (a) Give a general expression for all vectors in the range of A. What is the rank of A? (b) Using part (a), give a nonzero vector 6 for which Ax b is compatible. = (c) Give a vector 6 such that Ax = b is not compatible, and explain how you found b.
Transcribed Image Text:Exercise 3.4. Consider the matrix A - 3 2 -2 6 4 1 -1 (a) Give a general expression for all vectors in the range of A. What is the rank of A? (b) Using part (a), give a nonzero vector 6 for which Ax b is compatible. = (c) Give a vector 6 such that Ax = b is not compatible, and explain how you found b.
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