5. Let A Є Mnxn (F) be an invertible matrix, and let u E F" be a column vector. For each1≤i≤n let A,(u) be the matrix obtained from A by replacing the ith column of A with u. Also, let1xi=det A, (u)/ det A, and let x E F" be the column vector x =Show that Ax = u.In

Answered: Image /qna-images/answer/85582a13-de34-4336-b0cb-1d30eafeb4d5.jpg

Answered: 5. Let A Є Mnxn (F) be an invertible…

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