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| Math Central | Quandaries & Queries |
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Question from Jennifer, a student: Hello, my name is Jennifer. I am a 12th grader in Pre-Calculus and I was wondering if you may help me with Row Echelon Form. x + 2y - 3z = -5 |
Hi Jennifer,
The augmented matrix for this linear system is
\[ \left( \begin{array}{rrrr}
1
& 2 & -3 & -5\\
-2
& -4 & -6 & 10\\
3
& 7 & -2 & -13 \end{array} \right)\]
To make the first entry in the second row equal to $0$ I would multiply the first row by 2 and add to the second row. The result is
\[ \left( \begin{array}{rrrr}
1
& 2 & -3 & -5\\
0
& 0 & -12 & 0\\
3
& 7 & -2 & -13 \end{array} \right)\]
Wow!
Multiply the second row by $\large \frac{-1}{12}$ and the matrix becomes
\[ \left( \begin{array}{rrrr}
1
& 2 & -3 & -5\\
0
& 0 & 1 & 0\\
3
& 7 & -2 & -13 \end{array}. \right)\]
The second row is in the form you want for the third row so interchange the second and third row to get
\[ \left( \begin{array}{rrrr}
1
& 2 & -3 & -5\\
3
& 7 & -2 & -13\\
0
& 0 & 1 & 0 \end{array}. \right)\]
Can you see what to do now?
Penny
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