Prove as follows the inequality |Ax| =||A|| - |x|, where A is an m x m matrix with row vectors a1, a2, ..., am, and x is an m-dimensional vector. First note that the components of the vector Ax are aj · X, a2 • X, . .. , am • X, so 1/2 |Ax| = Σα2 Σ(a - x2 Then use the Cauchy-Schwarz inequality (a - x)? Ja2|x|? for the dot product. VI

Prove as follows the inequality |Ax| =||A|| - |x|, where A is an m x m matrix with row vectors a1, a2, ..., am, and x is an m-dimensional vector. First note that the components of the vector Ax are aj · X, a2 • X, . .. , am • X, so 1/2 |Ax| = Σα2 Σ(a - x2 Then use the Cauchy-Schwarz inequality (a - x)? Ja2|x|? for the dot product. VI

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...

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