(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

List the conditions of "a" under which the system:

x + ay - z = 1

-x + (a-2) y + z = -1

2x + 2y (a-2) z = 1

i) Has no solutions:

ii) Has a unique solution:

iii) Has infinite solutions.

The attempt at a solution

Well, I changed the matrix into reduced row-echelon form and I found:

x = (a-1)/a

y = 0

z = -1/a

The textbook gives the following answers:

i) No solutions: a = 0 (which I understand...because otherwise there would be an undefined x and z)

ii) Unique solution: a not= 0 and a not= 1, then unique solution of:

x = (a-1)/a

y = 0

z = -1/a (same as above)

iii) Infinite solutions: if a = 1, then solutions of x = -t, y = t, z = -1

-------------

I don't understand the third case for infinite solutions. If a = 1, then wouldn't: x = 0, y = 0, z = -1?

Also, what is the general strategy for solving such problems? (Many of these types of problems are given in the section of the textbook that I'm going through, yet no example was ever given.) I mean, I understand how to get a unique solution, and how to get no solution, but I'm not sure how you would deduce the case for infinite solutions.

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Algebra Concept Question

**Physics Forums | Science Articles, Homework Help, Discussion**