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5. Let A Є Mnxn (F) be an invertible matrix, and let u E F" be a column vector. For each 1≤i≤n let A,(u) be the matrix obtained from A by replacing the ith column of A with u. Also, let 1 xi= det A, (u)/ det A, and let x E F" be the column vector x = Show that Ax = u. In

5. Let A Є Mnxn (F) be an invertible matrix, and let u E F" be a column vector. For each 1≤i≤n let A,(u) be the matrix obtained from A by replacing the ith column of A with u. Also, let 1 xi= det A, (u)/ det A, and let x E F" be the column vector x = Show that Ax = u. In

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.3: Properties Of Determinants
Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
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5. Let A Є Mnxn (F) be an invertible matrix, and let u E F" be a column vector. For each 1≤i≤n let A,(u) be the matrix obtained from A by replacing the ith column of A with u. Also, let 1 xi= det A, (u)/ det A, and let x E F" be the column vector x = Show that Ax = u. In
Transcribed Image Text:5. Let A Є Mnxn (F) be an invertible matrix, and let u E F" be a column vector. For each 1≤i≤n let A,(u) be the matrix obtained from A by replacing the ith column of A with u. Also, let 1 xi= det A, (u)/ det A, and let x E F" be the column vector x = Show that Ax = u. In
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