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:

Depreciation Schedule

A table that shows the reduction in value of a company's assets over time.

Working Capital

The difference between a company's current assets and current liabilities, indicating the short-term financial health and operational efficiency.

Cost of Goods Sold

The direct costs attributable to the production of the goods sold by a company, including materials and labor.

Sales

The total amount of goods or services sold by a company, contributing to its revenue.