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ajayguhan
- 153
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I know that 3 x 3 determinant gives the volume of a parallelopiped, but how come after the row operations also it's gives the Same volume when it's elements are changed or in another words it's sides are being modified?
The determinant is a mathematical concept used to determine the properties of a matrix, such as its size, rank, and invertibility. It is calculated using a specific formula based on the elements of the matrix.
In a 3-dimensional space, a determinant can be calculated for a matrix representing the coordinates of three points. This determinant, known as the 3 x 3 determinant, gives the volume of the parallelepiped formed by these three points. It can also be used to calculate the volume of other 3-dimensional shapes, such as a cube or prism.
This is because the formula for calculating the 3 x 3 determinant involves finding the cross product of two vectors, which represents the area of a parallelogram. When this is multiplied by the third vector, it gives the volume of the parallelepiped formed by the three vectors.
No, the 3 x 3 determinant is specific to 3-dimensional space. However, the concept of determinants can be extended to higher dimensions, such as the 4 x 4 determinant for 4-dimensional space.
Yes, the 3 x 3 determinant is commonly used in physics and engineering to calculate the volume of irregularly shaped objects. It is also used in computer graphics to transform 3-dimensional objects in space. Additionally, it has applications in fields such as economics, chemistry, and biology.