# 307w.43.M40 find corresponding 3 scalars

• MHB
• karush
In summary, the conversation is about the row reduction of two matrices, B and C, and how they can be row-reduced to the same matrix. The process of row reduction is described and the conversation also discusses how the rows of one matrix can be written as a linear combination of the rows of the other matrix.
karush
Gold Member
MHB

ok did an image due to notation to be correct, we will be talking about this in the zoom class next week
but wanted to some grip of it before. Here is the RREFs
$\text{rref}(B)=\left[ \begin{array}{cccc} 1 & 0 & 7 & 0 \\ 0 & 1 & -3 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right]$
I assume we can switch c3 and c4 to get the triangle
and
 $\text{rref}(C)=\left[ \begin{array}{cccc} 1 & 0 & 7 & 0 \\ 0 & 1 & -3 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right]$

Last edited:
That looks good. You started with $B= \begin{bmatrix}1 & 3 & -2 & 2 \\ -1 & -2 & -1 & -1 \\ -1 & -5 & 8 & -3\end{bmatrix}$ and, I presume, added the first row to both second and third rows to get $\begin{bmatrix}1 & 3 & -2 & 2 \\ 0 & 1 & -3 & 1 \\ 0 & -2 & 6 & -1\end{bmatrix}$ and then add twice the second row to the third to get $\begin{bmatrix}1 & 3 & -2 & 2 \\ 0 & 1 & -3 & 1 \\ 0 & 0 & 0 & 1\end{bmatrix}$. Now subtract three times the new second row from the first row to get $\begin{bmatrix}1 & 0 & 7 & -1 \\ 0 & 1 & -3 & 1 \\ 0 & 0 & 0 & 1\end{bmatrix}$ and, finally, add the new third row to the first row and subtract the new third row from the second row to get $\begin{bmatrix}1 & 0 & 7 & 0 \\ 0 & 1 & -3 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix}$

And with $C= \begin{bmatrix}1 & 2 & 1 & 2 \\ 1 & 1 & 4 & 0 \\ -1 & -1 & -4 & 1 \end{bmatrix}$ I think I would first add the second row to the third, then subtract the first row from the second to get $\begin{bmatrix}1 & 2 & 1 & 2 \\ 0 & -1 & 3 & -2 \\ 0 & 0 & 0 & 1 \end{bmatrix}$. Subtract twice the third row from the first row and add twice the third row to the second row to get $\begin{bmatrix}1 & 2 & 1 & 0 \\ 0 & -1 & 3 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$. Finally, add twice the new second row to the first row, then multiply the second row by -1 to get $\begin{bmatrix}1 & 0 & 7 & 0 \\ 0 & 1 & -3 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$. Yes, the two matrices row-reduce to the same thing.

Now to do the rest of the exercise, write each row of B as a linear combination of rows of C, you can use each of those row-reductions. Each row of that row reduction is a linear combination of rows of C. For example the only change in the first row of C was when we added "twice the new second row to the first row" and the "new second row" was formed when we added "twice the third row to the second row". Writing the first, second, and third rows as $c_1$, $c_2$, and $c_2$, respectively, adding twice the third row to the second row gives $c_2+ 2c_3$ and adding twice that to first row gives $c_1+ 2(c_2+ 2c_3)= c_1+ cr_2+ 4c_3$. Do that for the second and third rows to get the rows of the common row-reduced matrix as linear combinations of the rows of C.

Do the same to get the rows of the common row reduced matrix in term of the rows of B, $b_1$, $b_2$, and $b_3$. Then set those equal to the expressions in terms of $c_1$, $c_2$, and $c_3$ and solve for $b_1$, $b_2$, and $b_3$ in terms of $c_1$, $c_2$, and $c_3$!

## 1. What is the purpose of finding corresponding 3 scalars in 307w.43.M40?

The purpose of finding corresponding 3 scalars in 307w.43.M40 is to identify the three scalar values that are associated with the given data set, which can be used for various calculations and analyses in scientific research.

## 2. How do you calculate the corresponding 3 scalars in 307w.43.M40?

The calculation of corresponding 3 scalars in 307w.43.M40 involves using mathematical equations and algorithms to determine the three scalar values that best fit the given data set. This process may vary depending on the specific data and the desired outcome.

## 3. What factors can affect the accuracy of finding corresponding 3 scalars in 307w.43.M40?

There are several factors that can affect the accuracy of finding corresponding 3 scalars in 307w.43.M40, including the quality and quantity of the data, the chosen mathematical model or algorithm, and potential errors or biases in the data collection process.

## 4. How can corresponding 3 scalars in 307w.43.M40 be used in scientific research?

Corresponding 3 scalars in 307w.43.M40 can be used in various ways in scientific research, such as for data analysis, predictive modeling, and hypothesis testing. They can also be used to identify patterns and relationships within the data and make predictions for future experiments or observations.

## 5. Are there any limitations to finding corresponding 3 scalars in 307w.43.M40?

Yes, there are limitations to finding corresponding 3 scalars in 307w.43.M40. This method may not be suitable for all types of data or research questions, and the results may not always be accurate or applicable in all situations. It is important to carefully consider the limitations and potential biases when using this approach in scientific research.

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