Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

So I am faced with the following: $$ \begin{align} x_1 + 4x_2 - 2x_3 +8x_4 &=12\\ x_2 - 7x_3 +2x_4 &=-4\\ 5x_3 -x_4 &=7\\ x_3 +3x_4 &=-5 \end{align}$$

How should I approach this problem? In other words, what is the next elementary row operation that I should attempt in order to solve it? I know how to do with 3 equations by using the augmented method but this got me a little confused.

share|improve this question
1  
Are you familiar with the method of Gaussian elimination? –  AWertheim Jun 5 '13 at 4:42

3 Answers 3

Write it as an augmented system:

$$\left[\begin{array}{cccc|c} 1& 4& -2& 8 & 12\\ 0& 1& -7& 2 & -4\\ 0& 0& 5& -1 & 7\\ 0& 0& 1& 3 & -5 \end{array}\right]$$

Gaussian Elimination (Row-Reduced-Echelon-Form - RREF) will yield:

$$\left[\begin{array}{cccc|c} 1& 0& 0& 0 & 2\\ 0& 1& 0& 0 & 7\\ 0& 0& 1 & 0 & 1\\ 0& 0& 0& 1 & -2 \end{array}\right]$$

Thus:

  • $x_4 = -2$
  • $x_3 = 1$
  • $x_2 = 7$
  • $x_1 = 2$
share|improve this answer
    
Putting matrices into the Latex area has been difficult for me, but it has been easy for you like drinking a glass of water. :D –  B. S. Jun 5 '13 at 7:14
    
@BabakS.: I created a little text file cheat sheet that I use for common LaTex items that I reuse because I am still too slow at typing things up and some of you are very fast! Feels like a time trial at times. Hope all is well with you my friend! Have a great day! –  Amzoti Jun 5 '13 at 12:16
    
I wish I could have that valuable cheat sheet. Wanna sell it? How many $?? :D –  B. S. Jun 5 '13 at 13:14
    
Cheat sheet to the rescue! +1 –  amWhy Jun 6 '13 at 0:21

HINT:

Use Elimination/ Substitution or Cross Multiplication to solve for $x_3,x_4$ from the last two simultaneous equation.

Putting the values of $x_3,x_4$ in the second equation, you will get $x_2$

Putting the values of $x_2,x_3,x_4$ in the first equation you will get $x_1$

share|improve this answer

By the Gauss-Jordan algorithm, your next step would be to make the $4x_{2}$ into a $0$, by the Type 3 elementary row operation: multiply row 2 by -4 and add that to row 1.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.