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The beginnings of matrices and determinants goes back to the second century BC although traces can be seen back to the fourth century BC. However, it was not until near the end of the 17th century that the ideas reappeared and development really go underway.
Matrices:
A set of numbers or objects or symbols represented in the form of rectangular array is called a matrix. The order of matrix is defined by the number of rows and number of columns present in the rectangular array of representation.
In simple words , A matrix is simply a set of numbers arranged in a rectangular table. We can add, substract, and multiply matrices together, under certain conditions.
Determinant:
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix. it is a real number associated with every square matrix. it is a real number and not a matrix. it can be a negative number. determinants only exist for square matrix.
The determinants can be viewed as a function whose input is a square matrix and whose output is a number.
The determinants is useful for solving linear equations, capturing how linear transformation change area or volume, and changing variables in integrals.