Use Matrices to Solve

question 69

Essay

Use matrices to solve $\left\{ \begin{array} { l } 12 x ^ { 2 } - 2 y ^ { 2 } + 8 z ^ { 2 } = 3 \\4 x ^ { 2 } + 7 y ^ { 2 } + 2 z ^ { 2 } = \frac { 17 } { 2 } \\2 x ^ { 2 } + 7 y ^ { 2 } - 4 z ^ { 2 } = \frac { 13 } { 2 }\end{array} \right.$

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Definitions:

Forest Tent Caterpillar

A species of moth larva that feeds on the leaves of deciduous trees, often creating large, communal webs or “tents” in the process.

Praying Mantis

A predatory insect known for its distinctive posture of folded forearms, contributing to pest control by consuming other insects.

Surface Fire

A fire that burns only the surface litter and undergrowth of a forest or grassland, often used in controlled burns for forest management.

Mature Trees

Fully grown trees that have reached their full size and reproductive potential, playing a crucial role in ecosystems by providing habitat and maintaining biodiversity.