4. Let A € Rnxn, u, v € Rn. Compute the inverse of A = 1 + uv¹. Hint: try a matrix I-auvT with a R to be determined. What constraint must u and v satisfy for the inverse to exist?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
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4. Let A € Rnxn, u, v € Rn. Compute the inverse of A = I + uvT. Hint:
try a matrix I - auvT with a R to be determined. What constraint
must u and v satisfy for the inverse to exist?
Transcribed Image Text:4. Let A € Rnxn, u, v € Rn. Compute the inverse of A = I + uvT. Hint: try a matrix I - auvT with a R to be determined. What constraint must u and v satisfy for the inverse to exist?
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