Elementary row operations question

In summary, the conversation discusses the steps taken to manipulate a given equation through different operations, including adding a multiple of one row to another, multiplying a row by a scalar, and adding the result to another row. The goal is to solve for the equation and end up with the correct answer. Despite initial confusion, the conversation eventually leads to the correct solution: 1 -2 3, 0 1 -3, 0 0 1.
  • #1
TonyC
86
0
I am working with the following equation:
|1 -2 3|
|6 -11 15|
|4 -14 21|
a. add -4 time Row1 to Row 3
b. add -6 times Row 1 to Row 2
c. add 6 times Row 2 to Row 3
d. multiply row 3 by -1/9

I have come up with the following answer:
|24 -48 72|
|180 -354 522|
|-19.99 39.99 -58.99|

Where did I go wrong?
 
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  • #2
Incidently, this is a multiple choice question and my answer isn't anywhere near any of the answers to choose from.
 
  • #3
After the 1st 2 operations, you should have ended up with,

Code: 
1 -2 3
0 1 -3
0 -6 9
 
  • #4
When you say first two operations, do you mean a and b or a?

What am I messing up?

After I ran a, I had:

-4 8 -12
6 -11 15
0 -6 9
 
  • #5
Why are you multiplying the first row by -4?
It says add -4 times Row 1 to Row 3.
Viet Dao,
 
  • #6
What does that mean?
Do I add -4 to Row 3 or do I multiply -4 by Row 1 than add Row 1 to Row 3?
 
  • #7
Add -4 times Row 1 To Row 3 means that you change Row 3 by adding -4 times Row 1 to it, and you don't change anything in Row 1, (ie: you just change Row 3).
Row 1 is: |1 -2 3|
-4 times Row 1 is : |-4 8 -12| (*)
You will add the (*) to row 3, which is:
|4 + (-4)xxxxxx-14 + 8xxxxxx21 + (-21)| = |0 -6 9|
You still keep Row 1. You only change Row 3. ie:
|1 -2 3|
|6 -11 15|
|0 -6 9|
Do the same for b, c, and d.
Viet Dao,
 
  • #8
OH, I SEE!

I have come up with:
1 -2 3
0 1 -3
0 0 1

THANK YOU!
 
  • #9
:smile: The light bulb has come on
 

Related to Elementary row operations question

1. What are elementary row operations?

Elementary row operations are a set of three operations that can be performed on a matrix in order to simplify it or solve a system of linear equations. These operations include multiplying a row by a non-zero constant, interchanging two rows, and adding a multiple of one row to another row.

2. How do I perform elementary row operations on a matrix?

To perform elementary row operations on a matrix, you must first identify which operation you need to perform and on which rows. Then, apply the operation to the matrix by multiplying the appropriate row by a constant, swapping two rows, or adding a multiple of one row to another row. Repeat this process until the desired matrix is achieved.

3. What is the purpose of using elementary row operations?

The purpose of using elementary row operations is to simplify a matrix or solve a system of linear equations. By performing these operations, the matrix is transformed into an equivalent matrix that is easier to work with and can provide useful information about the system of equations, such as a unique solution or inconsistency.

4. Are there any rules or restrictions when performing elementary row operations?

Yes, there are a few rules and restrictions to keep in mind when performing elementary row operations. First, the operations must be applied to the entire row, not just a single element. Second, the operations must be performed in a specific order: scaling, swapping, then adding. Third, the operations must be reversible, meaning the original matrix can be obtained by performing the inverse operations.

5. How do elementary row operations relate to Gaussian elimination?

Elementary row operations are the foundation of Gaussian elimination, a method used to solve a system of linear equations. By performing these operations on a matrix, Gaussian elimination transforms the matrix into a simpler form, ultimately leading to a matrix in reduced row echelon form which can provide the solution to the system of equations.

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