# 307.1.1 Use row reduction on the appropriate augmented

• MHB
• karush
In summary, the conversation discusses the process of using row reduction on a matrix to solve a system of equations. The augmented matrix is shown and the steps for reducing it to a simpler form are explained. The final solution is given as x = 4/5 and y = -1/5. There is also a mention of calculators and their role in simplifying the process of matrix reduction.
karush
Gold Member
MHB
$\tiny{307.1.1}$
Use row reduction on the appropriate augmented matrix to solve the following system of equations:
$\begin{array}{ll}3x+2y&=2\\x-y&=1\end{array} \sim\left[\begin{array}{rr|r}3&2&2\\ \:1&-1&1\end{array}\right]\sim \begin{bmatrix}1&0&\frac{4}{5}\\ 0&1&-\frac{1}{5}\end{bmatrix}$

$x=\dfrac{4}{5}\quad y= -\dfrac{1}{5}$

hopefully no typos!
suggestions??

Last edited:
Well, 3(4/5)+ 2(-1/5)= 12/5- 2/5= 10/5= 2
and 4/5- (-1/5)= 4/5+ 1/5= 5/5= 1

So you certainly got the right answers!

as simple as it looks the steps were very confusing
spent over an hour on it

karush said:
as simple as it looks the steps were very confusing
spent over an hour on it

reduction of matrices is arithmetic torture ...that's why calculators were invented

I don't consider it that bad. It's mostly just a matter of practice like arithmetic.
$\begin{array}{c}-3\\*\end{array}\left[\begin{array}{cc|c}3&2&2\\1&-1&1\end{array}\right] \to \updownarrow\left[\begin{array}{cc|c}0&5&-1\\1&-1&1\end{array}\right] \to \begin{array}{c}\\*\frac 15\end{array}\left[\begin{array}{cc|c}1&-1&1\\0&5&-1\end{array}\right] \to \begin{array}{c}+1\\*\end{array}\left[\begin{array}{cc|c}1&-1&1\\0&1&-\frac 15\end{array}\right] \to \left[\begin{array}{cc|c}1&0&\frac 45\\0&1&-\frac 15\end{array}\right]$

skeeter said:
reduction of matrices is arithmetic torture ...that's why calculators were invented

https://www.physicsforums.com/attachments/10876
View attachment 10877
\looks like a TI

I had a a TI CAS but loaned it out never got it back

## 1. What is the purpose of using row reduction in scientific research?

The purpose of using row reduction in scientific research is to simplify a system of equations and solve for unknown variables. This process is commonly used in linear algebra and can help researchers analyze and interpret data more efficiently.

## 2. How does row reduction work?

Row reduction involves applying a series of elementary row operations, such as swapping rows, multiplying rows by a constant, or adding a multiple of one row to another, to a matrix. These operations are used to transform the matrix into a simpler form, such as row echelon form or reduced row echelon form, making it easier to solve for the unknown variables.

## 3. When should row reduction be used in scientific experiments?

Row reduction should be used when a system of equations needs to be solved for unknown variables. This can occur in various scientific experiments, such as analyzing data from chemical reactions or studying the behavior of physical systems.

## 4. What are the advantages of using row reduction?

One of the main advantages of using row reduction is that it simplifies complex systems of equations, making them easier to solve and interpret. It also allows researchers to identify patterns and relationships within the data, which can lead to further insights and discoveries.

## 5. Are there any limitations to using row reduction in scientific research?

While row reduction can be a powerful tool in solving equations, it may not always be applicable or efficient in all scientific research. For example, it may not be suitable for non-linear systems or systems with a large number of variables. In these cases, alternative methods may need to be used.

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