SOLUTION: Hi, I'm having trouble with this question. I don't know how I'm supposed to work it out, so any help would be great appreciated! Thank you! Determine the values for "a" for whic

Algebra ->  Matrices-and-determiminant -> SOLUTION: Hi, I'm having trouble with this question. I don't know how I'm supposed to work it out, so any help would be great appreciated! Thank you! Determine the values for "a" for whic      Log On


   

Question 1050347: Hi, I'm having trouble with this question. I don't know how I'm supposed to work it out, so any help would be great appreciated! Thank you!
Determine the values for "a" for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. I need to solve using a matrix, and then row reducing.
3X1 + aX2 + 6X3 = 6
-X1 + 3X2 - X3 = 1
2X1 - 2X2 + 6X3 = 11
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%28matrix%283%2C4%2C3%2Ca%2C6%2C6%2C-1%2C3%2C+-1%2C1%2C2%2C-2%2C6%2C11%29%29
~%28matrix%283%2C4%2C0%2Ca%2B9%2C3%2C9%2C-1%2C3%2C+-1%2C1%2C0%2C1%2C1%2C13%2F4%29%29, after 3R%5B2%5D%2BR%5B1%5D and 2R%5B2%5D%2BR%5B3%5D,
~%28matrix%283%2C4%2C1%2C-3%2C+1%2C-1%2C0%2C1%2C1%2C13%2F4%2C0%2Ca%2B9%2C3%2C9%29%29
~, after -%28a%2B9%29R%5B2%5D%2BR%5B3%5D.
(We may assume that a%2B9%3C%3E0. If a+9=0, or a = -9, then the system will have a unique solution.)

Case 1. -a-6 = 0. ===> a = -6.
===> -13a%2F4+-+81%2F4+=+-3%2F4++%3C%3E+0
===> System has no solution.

Case 2. -a-6+%3C%3E+0 ===> a%3C%3E-6 ===> ===> System has unique solution.

There is no instance that the system will have infinite number of solutions.