In Order for a Matrix a to Have an Inverse $\left( \begin{array} { r r } 3 & 6 \\- 2 & 1\end{array} \right)$

question 34

Essay

In order for a matrix A to have an inverse, its determinant cannot be zero. Derive the determinant of the following matrices:
A = $\left( \begin{array} { r r } 3 & 6 \\- 2 & 1\end{array} \right)$ B = $\left( \begin{array} { r r r } 1 & - 1 & 2 \\1 & 0 & 3 \\4 & 0 & 2\end{array} \right)$ X'X where X = (1 10)

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Definitions:

Intrusive Area

An intrusive area is a region where igneous rocks have crystallized from magma intruding into the Earth's crust but have not erupted onto the surface.

Source Area

The geographic location where the materials of a sedimentary rock were derived from.

Radioactive Decay

The process by which an unstable atomic nucleus loses energy by emitting radiation, leading to a change in the number and/or arrangement of its protons and neutrons.

Conduction

The direct transfer of heat or electricity through a substance when there is a temperature or electrical potential difference.