Determinant of a matrix

EXAMPLE: Finding the determinant of a matrix by first doing row operations - Duration: 8:49. Determinant of a Matrix is a number that is specially defined only for square matrices. But there are other methods (just so you know).

It is equal to zero for all non-square matrices. The determinant of a matrix has various applications in the field of mathematics including use with systems of linear equations, finding the inverse of a matrix, and calculus.

The determinant of a square matrix A is the integer obtained through a range of methods using the elements of the matrix.

The determinant of a matrix is a number that is specially defined only for square matrices. Determinant The determinant of an n x n square matrix A, denoted |A| or det (A), in one of its simpler definitions, is a value that can be calculated from a square matrix .

To every square matrix A = [aij] of order n, we can associate a number (real or complex) called determinant of the square matrix A, where a = (i, j)If M is the set of square matrices, K is the set of numbers (real or complex) and f : M → K is defined by f (A) = k, where A ∈ M and k ∈ K, then f (A) is called the determinant of A. The determinant of a matrix is a A The determinant of that matrix is (calculations are explained later):The determinant helps us find the The Example:(Exactly the same symbol as First of all the matrix must be For a The determinant is:It is easy to remember when you think of a cross: For a The determinant is:It may look complicated, butTo work out the determinant of a As a formula The pattern continues for As a formula:Notice the  The pattern continues for  This method of calculation is called the "Laplace expansion" and I like it because the pattern is easy to remember. The determinant is useful for solving linear equations, capturing how linear transformation change area or volume , and changing variables in integrals. It is also denoted by | A | or det A or Δ.$$ If A =\begin{bmatrix}  a & b \\ c & d \end{bmatrix}, then \ determinant \ of \ A \ is \ written \ as \ |A| \ =\begin{vmatrix}  a & b \\ c & d \end{vmatrix} = det A $$ Let A = [a] be the matrix of order 1, then determinant of A is defined to be equal to a.For a The determinant is: Example: $$ If A =\begin{bmatrix}  2 & 3 \\ 4 & 8 \end{bmatrix}$$|A| = 2 x 8 – 4 x 3For a The determinant is: To work out the determinant of a matrix 3×3:As a The determinant of A equals ‘a’ times the determinant of e The pattern continues for the determinant of a matrix As a formula:Notice the +−+− pattern (+a… −b… +c… −d…).Is determinant available just for square matrix?Yes, it is only defined for square matrices.It actually is.

.