Solving simultaneous equations

  • Thread starter lavster
  • Start date
  • #1
217
0
when solving a system of simultaneous equations in matrix from (with the LHS = 0) why does the determinant of the matrix need to vanish?

thanks
 

Answers and Replies

  • #2
34,530
6,226
when solving a system of simultaneous equations in matrix from (with the LHS = 0) why does the determinant of the matrix need to vanish?

thanks
I'm guessing you're talking about a matrix equation Ax = 0, where A is an n x n matrix containing the coefficients of the variables, x is a column vector with n entries, and 0 is a column vector whose n entries are all zero. (BTW, you almost always see the zero vector on the right side of the equation, not the left.)

For a unique solution to the system, the determinant of A must be nonzero; i.e., must NOT vanish. If det(A) is not zero, then A has an inverse, so the solution to the system is obtained by multiplying both sides of the equation by A-1.

Ax = 0 ==> A-1Ax = A-10 == > x = 0

If the determinant of A vanishes (i.e., det(A) = 0), then A does not have an inverse, which means in this case that there are an infinite number of solutions.
 

Related Threads on Solving simultaneous equations

  • Last Post
Replies
4
Views
693
  • Last Post
Replies
21
Views
2K
Replies
1
Views
2K
Replies
9
Views
905
Replies
10
Views
9K
Replies
7
Views
3K
Replies
6
Views
821
Replies
2
Views
1K
Replies
7
Views
5K
  • Last Post
Replies
1
Views
2K
Top