Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
The complete question is:
Create a matrix for this linear system:
what is the solution of the system?
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
The solution straight from the matrix as
[tex]${data-answer}amp;x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]${data-answer}amp;y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]
and z = r
What is the solution of the system?
A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.
Given:
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
By applying two more row operations, we get
[tex]${data-answer}amp;{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]
simplifying the above matrix, we get
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]
[tex]${data-answer}amp;\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$[/tex]
The solution straight from the matrix as
[tex]${data-answer}amp;x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]${data-answer}amp;y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and
z = r
To learn more about matrix refer to:
brainly.com/question/24511230
#SPJ4
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
