What is the area of the parallelogram defined by the columns of matrix ?
Area Ex: 1

To find the area of the parallelogram defined by the columns of the given matrix, you can use the determinant of the matrix. The determinant is calculated as follows for the matrix :

So, the area of the parallelogram is 18.

Even in ancient times, civilizations such as the Egyptians and Babylonians were effectively using concepts of geometry to solve problems related to areas and volumes, reflecting a rich history of mathematical inquiry. They didn’t have matrices or determinants but had their own clever ways of calculating the area of shapes like rectangles and triangles, laying the groundwork for the amazing mathematical advances we enjoy today.

In practical scenarios, parallelograms can be found everywhere, from architecture to engineering designs. For example, when designing a building, engineers might use the concept of parallelograms to ensure the structure distributes weight evenly. Knowing how to calculate areas helps architects maximize space and ensure stability, proving that math truly underpins the world around us.