Show That the Given Matrix Is Positive Definite, and Then

question 4

Essay

Show that the given matrix is positive definite, and then find the LDU-factorization.

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Definitions:

Physical World

The aspects of the universe that are capable of being observed and studied, encompassing natural, material phenomena.

Cell Expansion

The process by which a cell increases in size, often involving the intake of water and growth of the cell wall and membrane.

Pattern Formation

The biological process by which cells in a developing organism acquire different identities, leading to the formation of specific tissues, organs, and overall body plan.

Differential Gene Expression

The process where genes are turned on or off in different cell types, leading to differences in structure and function among cells.