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System of equations

  • #1

Homework Statement


Under what condition will the following system have a unique solution?

x -y +2z = 1
ax -ay +4z = 2a
x +y +az = 4

Note: a is a parameter.



The Attempt at a Solution


I know I'm supposed to solve by turning this into the identity matrix by I really have no idea where to start. Hellp would be much appreciated.
 

Answers and Replies

  • #2
UltrafastPED
Science Advisor
Gold Member
1,912
216
Rewrite the equation in matrix form:

1 -1 2 x 1
a -a 4 * y = 2a
1 1 a z 4

This system is has a unique solution if the matrix on the LHS has an inverse.

From your (3) it seems that you are to use Gaussian elimination:
http://en.wikipedia.org/wiki/Gaussian_elimination

Depending on how you set this up it can provide the inverse matrix and the solution.
 
  • #3
Rewrite the equation in matrix form:

1 -1 2 x 1
a -a 4 * y = 2a
1 1 a z 4

This system is has a unique solution if the matrix on the LHS has an inverse.

From your (3) it seems that you are to use Gaussian elimination:
http://en.wikipedia.org/wiki/Gaussian_elimination

Depending on how you set this up it can provide the inverse matrix and the solution.
Can I ignore the right side of all the equations in order to find the inverse?
 
  • #4
33,505
5,191
Yes.
 

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