stomlin108
New member
- Joined
- Jul 5, 2010
- Messages
- 2
Given that (c1, c2, c3 ) is a solution of the following homogeneous system of equations:
a11x1 + a12x2 + a13x2 = 0
a21x1 + a22x2 + a23x2 = 0
a31x1 + a32x2 + a33x2 = 0
Demonstrate that for any real number k (k1, k2, k3 ) is also a solution.
I am not sure how to demonstrate this. I am guessing that unless C1, C2, C3 is zero, that there would be infinitely many solutions. Do I set the second two problems up as paramtetric solution, such as
c1=-S-T
c2=S
c3=T
for all real numbers S and T
then plug in k1, k2, k3 to show that it is also a solution?
As you can see, I am confused! I can do the work with numbers, but am confused with the letters
a11x1 + a12x2 + a13x2 = 0
a21x1 + a22x2 + a23x2 = 0
a31x1 + a32x2 + a33x2 = 0
Demonstrate that for any real number k (k1, k2, k3 ) is also a solution.
I am not sure how to demonstrate this. I am guessing that unless C1, C2, C3 is zero, that there would be infinitely many solutions. Do I set the second two problems up as paramtetric solution, such as
c1=-S-T
c2=S
c3=T
for all real numbers S and T
then plug in k1, k2, k3 to show that it is also a solution?
As you can see, I am confused! I can do the work with numbers, but am confused with the letters