#Matrices
Determine b such that the system of homogeneous equation
2x+y+2z=0
x+y+3z=0
4x+3y+bz=0
has trivial solution
This problem is taken from HK Das Book Page# 72
and solution by book is
For trivial solution We know that x=0,y=0 and z=0.So b can have any value but i have the point that
For homogeneous solution,
Rank of A= n(no of unknowns) as per book
Here no of unknown is three(x,y,z)
and if we solve the matrix
2 1 2
1 1 3
4 3 b
then matrix is like this
1 1 3
0 -1 -4
0 0 b-8
So according to me b is not equal to 8 for unique or trivial solution as per definition Rank of A=n(no of unknowns) for unique solution but book said anyvalue of b
Please tell if anyone know.
Thanks in advance.