Question

how do you find the determinant of the matrix?

Answer 1

The determinant of a square matrix is a fundamental scalar associated to
this matrix with a long mathematical history......
he can be useful to know if the matrix is invetible or not...and calculate the inverse sometimes....
To find it...there isn't a specific way ..for.2 by 2 or3by3 matrix..to calculate the determinant it's "easy"...but in the general case, it depends on the problems...

Answer 2

You can calculate the determinant of an arbitrary matrix by expanding it in minors,
which reduces the determinant of an n by n matrix to a sum over n determinants
of n-1 by n-1 matrices. Eventually, yopu'll reduce it to 2 by 2.....

Answer 3

@fwizbang usually, It gets complicated ! doing about n! operation ! so;personally ; I never calculate it like that before !

Answer 4

True enough. Generally, it's good to avoid calculating the determinant if you can,
but if you can't .....

Answer 5

Another fairly easy way to find the determinant is to perform elimination on the matrix to find U, and then simply multiply all pivots to find the determinant. Therefore, if the determinant is 0, there was a 0 pivot somewhere in the matrix, proving that it is singular.