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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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