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Problem 3 Let A and B be symmetric positive definite nx n matrices, and let x, y e R" with x + 0 and y # 0. Are the following statements true or false? Circle your answer. If true, it needs to be true for all positive definite A, B, and all nonzero x, y. (A) TRUE – FALSE AA + BB is positive definite. (B) TRUE - FALSE (x+y)" A(x+ y) 2r' Ax+y" Ay (C) TRUE- FALSE tr(ABA-) >0 (D) TRUE - FALSE B is invertible. (E) TRUE FALSE B- is no longer symmetric.

Problem 3 Let A and B be symmetric positive definite nx n matrices, and let x, y e R" with x + 0 and y # 0. Are the following statements true or false? Circle your answer. If true, it needs to be true for all positive definite A, B, and all nonzero x, y. (A) TRUE – FALSE AA + BB is positive definite. (B) TRUE - FALSE (x+y)" A(x+ y) 2r' Ax+y" Ay (C) TRUE- FALSE tr(ABA-) >0 (D) TRUE - FALSE B is invertible. (E) TRUE FALSE B- is no longer symmetric.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 26E
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Problem 3 Let A and B be symmetric positive definite n x n matrices, and let x, y e R" with x # 0 and y # 0. Are the following statements true or false? Circle your answer. If true, it needs to be true for all positive definite A, B, and all nonzero x, y. (A) TRUE – FALSE AA+ BB is positive definite. (B) TRUE – FALSE (x+y)" A(x + y) 2 x Ax + y" Ay (C) TRUE - FALSE tr(ABA-l) > 0 (D) TRUE - FALSE B is invertible. (E) TRUE – FALSE B- is no longer symmetric.
Transcribed Image Text:Problem 3 Let A and B be symmetric positive definite n x n matrices, and let x, y e R" with x # 0 and y # 0. Are the following statements true or false? Circle your answer. If true, it needs to be true for all positive definite A, B, and all nonzero x, y. (A) TRUE – FALSE AA+ BB is positive definite. (B) TRUE – FALSE (x+y)" A(x + y) 2 x Ax + y" Ay (C) TRUE - FALSE tr(ABA-l) > 0 (D) TRUE - FALSE B is invertible. (E) TRUE – FALSE B- is no longer symmetric.
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