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Suppose A is an x n matrix. (a) If ker(A) = (b) Give an example of a matrix with ker(A) = im(A). im(A), what is A²? Explain.

Suppose A is an x n matrix. (a) If ker(A) = (b) Give an example of a matrix with ker(A) = im(A). im(A), what is A²? Explain.

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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Suppose \( A \) is a \( n \times n \) matrix. (a) If \( \ker(A) = \operatorname{im}(A) \), what is \( A^2 \)? Explain. (b) Give an example of a matrix with \( \ker(A) = \operatorname{im}(A) \).
Transcribed Image Text:Suppose \( A \) is a \( n \times n \) matrix. (a) If \( \ker(A) = \operatorname{im}(A) \), what is \( A^2 \)? Explain. (b) Give an example of a matrix with \( \ker(A) = \operatorname{im}(A) \).
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