Join the IDNLearn.com community and get your questions answered by experts. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.
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
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.
