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Suppose that C is an n x n matrix that I is an n x n identity matrix, and det (CI) = 0 Show that there is some nonzero n × 1 column matrix b so that Cb=b.

Suppose that C is an n x n matrix that I is an n x n identity matrix, and det (CI) = 0 Show that there is some nonzero n × 1 column matrix b so that Cb=b.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.2: Addition And Subtraction Of Matrices
Problem 13E
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Suppose that C is an n x n matrix that I is an n x n identity matrix, and det (CI) = 0 Show that there is some nonzero n × 1 column matrix b so that Cb=b.
Transcribed Image Text:Suppose that C is an n x n matrix that I is an n x n identity matrix, and det (CI) = 0 Show that there is some nonzero n × 1 column matrix b so that Cb=b.
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