Matrix and determinant//examples solved @ChemistryZone809

Matrices and determinants are fundamental concepts in linear algebra. Here's a brief overview:

*Matrices:*

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example:

| 1 2 3 |
| 4 5 6 |
| 7 8 9 |

Matrices can be used to represent systems of linear equations, linear transformations, and more.

*Determinants:*

The determinant of a square matrix (a matrix with the same number of rows and columns) is a scalar value that can be computed from the matrix's elements. It's denoted as det(A) or |A|.

The determinant has several key properties:

1. *Zero determinant*: If the determinant is zero, the matrix is singular (not invertible).
2. *Non-zero determinant*: If the determinant is non-zero, the matrix is invertible.
3. *Scalar multiplication*: The determinant of a matrix scaled by a scalar is equal to the scalar raised to the power of the matrix's dimension, multiplied by the original determinant.

Determinants are used in various applications, such as:

1. *Solving systems of linear equations*
2. *Finding the inverse of a matrix*
3. *Calculating the area or volume of a parallelogram or parallelepiped*