Finding the value of a variable in a matrix

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1. Oct 20, 2014

incxx

1. The problem statement, all variables and given/known data
Given :

 x+y+5z = 2

 x+2y+7z = 1

 2x−y+4z = a
.
a) Determine the value of a which will make the given system have many solutions. Explain your answer.
b) Choose a value of a which will make the given system have NO solutions. Explain your answer.
c) Is it possible to choose a value of a, which will make the given system have exactly one solutions? Explain

2. Relevant equations

3. The attempt at a solution
I found the reduced matrix of the system of equations and got,
1 0 3
0 1 2
0 0 0
, but am not sure on what to do next.

2. Oct 21, 2014

Staff: Mentor

You need to set up an augmented matrix whose fourth column contains the constants on the right sides of your equations.

3. Oct 21, 2014

HallsofIvy

Staff Emeritus
Equivalently, don't use matrices at all!
You have:
x+y+5z = 2
 x+2y+7z = 1
 2x−y+4z = a

Subtract the first equation from the second to get y+ 2z= -1.
Subtract the third equation from twice the first equation to get 3y+ 6z= 4- a

Subtract three times the first of those equations from the second to get 0= 7- a.

For what value of a is that true? So for what value of a does the original set of equations have an infinite number or solutions? For what values of a does it have no solution?

4. Oct 21, 2014

incxx

thank you I understand how to do it now!