Question

Select the correct answer. create a matrix for this linear system: what is the solution of the system?

Answer 1

The complete question is:

Create a matrix for this linear system:

what is the solution of the system?

$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$

The solution straight from the matrix as

$&x=\frac{1}{5}+\frac{7}{5} r$

$&y=-\frac{4}{5}-\frac{3}{5} r$

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:

$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$

By applying two more row operations, we get

$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}}$

$&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2}$

simplifying the above matrix, we get

$&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1}$

$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$

The solution straight from the matrix as

$&x=\frac{1}{5}+\frac{7}{5} r$

$&y=-\frac{4}{5}-\frac{3}{5} r$ and

z = r

To learn more about matrix refer to:

brainly.com/question/24511230

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