Find an Orthogonal Matrix P and Diagonal Matrix D Such

question 22

Essay

Find an
orthogonal matrix P and diagonal matrix D such that the change of variables
transforms the given quadratic form
into the form

.

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Definitions:

Illiterate Field Hands

Agricultural workers, often slaves or laborers in later periods, who could not read or write, common on plantations and farms historically.

Negotiate

The process of discussing something with someone in order to reach an agreement or mutual understanding.

Plains of Chalmette

The site of the Battle of New Orleans in 1815, a significant American victory at the end of the War of 1812.

Battle of New Orleans

A significant battle fought between British and American forces in 1815, marking the end of the War of 1812 and resulting in a decisive American victory, boosting national pride.