Linear Algebra And Matrix

Question

Determine the value of k for which the system

 

x+y+2z=0

x+2y-3z=-2

3x+9y+kz=-11

 

has no solutions.

 

so, what's k = ?

Answer 1

Set the principal determinant of the system equal to zero, and solve for k.  The principal determinant is

 

|1  1  2|

|1  2 -3|

|3  9  k|

 

Set it equal to zero and solve for k.  You should be able to finish from here.