Linear Algebra Question

  • Thread starter CaityAnn
  • Start date
  • #1
38
0
I have three systems of equations:
x+y+2z=a , x+z= b and 2x+y+3z=c
Show that in order for this system to have at least one solution, a,b,c must satisfy c=a+b.

Obviously I can add the equations a and b and get c. But I dont know how else to approach showing this. I think the points of x,y,z of c must satisfy both a,b and provide a solution set for both but Im not sure how to prove that. HELP PLEASE~!
 

Answers and Replies

  • #2
1,235
1
The matrix system is:

[tex] \begin{bmatrix}
1 & 1 & 2 & a \\
1 & 0 & 1 & b \\
2 & 1 & 3 & c \\
\end{bmatrix}[/tex]

The system has at least one solution if the rank of the coefficient matrix equals the rank of the augmented matrix. Get the matrix to row-echleon form.
 
Last edited:

Related Threads on Linear Algebra Question

  • Last Post
Replies
1
Views
770
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
741
  • Last Post
Replies
1
Views
871
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
808
  • Last Post
Replies
6
Views
931
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
Top