The discussion revolves around solving a system of three equations involving the variable alpha(a) to demonstrate that it has two non-trivial solutions. The equations are represented in matrix form as AX = 0, where A is the coefficient matrix. The key to finding the values of a that lead to non-invertibility of matrix A lies in determining when the determinant of A equals zero or through row-reduction methods. The participant is encouraged to explore these methods to identify the required values of a.
PREREQUISITESStudents studying linear algebra, educators teaching matrix theory, and anyone interested in solving systems of equations involving parameters.
Well, what HAVE you done? You mention "unknowns in a matrix" so presumably you know how to set this up as a matrix equation. With A as the matrix of coefficients, X as the column matrix <x, y, z> and 0 as the column matrix <0, 0, 0>, your equation is AX= 0. The unique solution will be [itex]X= A^{-1}0= 0[/itex] as long as A has an inverse.Martinuk said:Homework Statement
the following 3 equations are given, show that alpha(a) has two non trival solutions, then solve for the whole thing:
Homework Equations
ax - 3y + ( 1+a) z = 0
2x + y - az = 0
(a+2)x - 2y + az = 0
i think i may be missing something but i can't seem to even get started on this problem,
thanks