Finding the amount of solutions in a 3 equation solution x + 2 y +...

Quintin Stafford

Quintin Stafford

Answered

2022-06-24

Finding the amount of solutions in a 3 equation solution
x + 2 y + 3 z = 7
3 x + 4 y z = 4
3 x + 2 y 11 z = 13

Answer & Explanation

Elianna Douglas

Elianna Douglas

Expert

2022-06-25Added 23 answers

We have the system
x + 2 y + 3 z = 7
3 x + 4 y z = 4
3 x + 2 y 11 z = 13
The associated augmented coefficient matrix is given by:
( 1 2 3 | 7 3 4 1 | 4 3 2 11 | 13 )
Use Gaussian Elimination (row reduction using elementary row operations). If you encounter a row with all zeros, then you'll know there are infinitely many solutions. You'll have an inconsistent system, for which there are NO solutions, if you obtain a row such as
( 0 0 0 | a )
where a 0. Otherwise, the system will have one unique solution.
If you row reduce correctly, you should obtain a reduced row form as follows:
( 1 0 7 | 10 0 1 5 | 17 2 0 0 0 | 0 )
flightwingsd2

flightwingsd2

Expert

2022-06-26Added 5 answers

[ 1 2 3 7 3 4 1 4 3 2 11 13 ]
[ 1 2 3 7 0 2 10 17 0 4 20 34 ]
[ 1 2 3 7 0 2 10 17 0 0 0 0 ]
0 = 0
Infinite amount of solutions

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?