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6. Determine the definiteness of the following symmetric matrices. -1 1 1 -1 0 0\ (1 2 oy 2 4 5 0 5 64

6. Determine the definiteness of the following symmetric matrices. -1 1 1 -1 0 0\ (1 2 oy 2 4 5 0 5 64

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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5. Consider the case of throwing two coins. The probability space is {HH,HT,TH,TT}. The random variable that the first dice is 1 is X = (1,1,0,0). The random variable that the second dice is 1 is Y = (1,0,1,0). Show the centered random variables of X and Y are orthogonal. [Note: These random variable are actually independent.] 6. Determine the definiteness of the following symmetric matrices. (1 2 oy -1 0 ),2 4 5 lo 5 6/ 1 7. Suppose A is a 4 x 4 matrix. Give the determinant conditions for checking each of the following cases. a. A is positive definite. b. A is negative definite. c. A is positive semidefinite. d. A is negative semidefinite.
Transcribed Image Text:5. Consider the case of throwing two coins. The probability space is {HH,HT,TH,TT}. The random variable that the first dice is 1 is X = (1,1,0,0). The random variable that the second dice is 1 is Y = (1,0,1,0). Show the centered random variables of X and Y are orthogonal. [Note: These random variable are actually independent.] 6. Determine the definiteness of the following symmetric matrices. (1 2 oy -1 0 ),2 4 5 lo 5 6/ 1 7. Suppose A is a 4 x 4 matrix. Give the determinant conditions for checking each of the following cases. a. A is positive definite. b. A is negative definite. c. A is positive semidefinite. d. A is negative semidefinite.
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