Show That the Given Symmetric Matrix a Is Positive Definite

question 65

Essay

Show that the given symmetric matrix A is positive definite by finding the determinants of its leading principal submatrices. Then find the LDU-factorization of A.

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Definitions:

Draining Blood

The process of removing blood from the body, typically done for medical reasons such as to relieve pressure from a hematoma or in therapeutic phlebotomy.

Diastolic Pressure

The lower number in a blood pressure reading, representing the pressure in the arteries when the heart rests between beats.

Systolic Pressure

The highest blood pressure measured in the arteries during the contraction phase of the heart cycle.

Korotkoff Sounds

Sounds heard over an artery when blood pressure is determined by the auscultatory method; caused by turbulent flow of blood.