Augment Matrix with Unknowns.....help !! thanks

[fruzmatik]

I am havin alot of problems trying to reduce this properly and answer teh following questios...thanks for the help!!!



consider the following linear system in x; y and z:
x + y + az = 2
2x + y + 2az = 3
3x + y + 3az = c
Note that the general solution of this system may depend on the values of a and c.

(a) If [A| b ] denotes the augmented matrix of the system above, the rank of A and the rank of [A| b ] will
depend on the values of a and c. Find, for all values of a and c,
(i) rank (A), and
(ii) rank [A|b]

(b) Find all values of a and c so that this system has
(i) a unique solution,
(ii) infinitely many solutions, or
(iii) no solutions.
(c) In case b(ii) above, give the general solution.

 

[pka]

Are you sure that you have presented the problem correctly?
Because, for every value of a the matrix of coefficients is singular!
Therefore, the questions really don’t work.