F1.6 Question 9 on paper ### Linear Systems and Row Echelon FormIn this section, we'll explore solving linear systems by reducing an augmented matrix to its reduced row echelon form. You will practice these skills in the exercises provided.#### ExampleConsider the linear system represented in matrix form:\[ \begin{pmatrix}1 & 2 & 3 \\1 & 5 & -5 \\3 & 5 & 8\end{pmatrix}\begin{pmatrix}x_1 \\x_2 \\x_3\end{pmatrix}=\begin{pmatrix}b_1 \\b_2 \\b_3\end{pmatrix}\]**Exercises 7 and 8: Solve the linear systems given.**7. \[\begin{cases}3x_1 + 5x_2 = b_1 \\x_1 + 2x_2 = b_2\end{cases}\]8. \[\begin{cases}x_1 + 2x_2 + 3x_3 = b_1 \\2x_1 + 5x_2 - 5x_3 = b_2 \\3x_1 + 5x_2 + 8x_3 = b_3\end{cases}\]**In Exercises 9-12, solve the linear systems. Using the given values for the \(b\)'s solve the systems together by reducing an appropriate augmented matrix to reduced row echelon form.**9. \[\begin{cases}x_1 - 5x_2 = b_1 \\3x_1 + 2x_2 = b_2\end{cases}\]For part (i) \(b_1 = 1, b_2 = 4\)For part (ii) \(b_1 = -2, b_2 = 5\)10. \[\begin{cases}-x_1 + 4x_2 + x_3 = b_1 \\x_1 + 9x_2 - 2x_3 = b_2 \\6x_1 + 4x_2 - 8x_3 = b_3\end{cases}\

Answered: In Exercises 9-12, solve the lin the…

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In Exercises 9-12, solve the lin the b's solve the systems toget Ma ond

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Matrices And Determinants

Section: Chapter Questions

Problem 15T: One hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a...

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Question

F1.6 Question 9 on paper

### Linear Systems and Row Echelon Form

In this section, we'll explore solving linear systems by reducing an augmented matrix to its reduced row echelon form. You will practice these skills in the exercises provided.

#### Example
Consider the linear system represented in matrix form:
\[
\begin{pmatrix}
1 & 2 & 3 \\
1 & 5 & -5 \\
3 & 5 & 8
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2 \\
x_3
\end{pmatrix}
=
\begin{pmatrix}
b_1 \\
b_2 \\
b_3
\end{pmatrix}
\]

**Exercises 7 and 8: Solve the linear systems given.**

7.
\[
\begin{cases}
3x_1 + 5x_2 = b_1 \\
x_1 + 2x_2 = b_2
\end{cases}
\]

8.
\[
\begin{cases}
x_1 + 2x_2 + 3x_3 = b_1 \\
2x_1 + 5x_2 - 5x_3 = b_2 \\
3x_1 + 5x_2 + 8x_3 = b_3
\end{cases}
\]

**In Exercises 9-12, solve the linear systems. Using the given values for the \(b\)'s solve the systems together by reducing an appropriate augmented matrix to reduced row echelon form.**

9.
\[
\begin{cases}
x_1 - 5x_2 = b_1 \\
3x_1 + 2x_2 = b_2
\end{cases}
\]

For part (i) \(b_1 = 1, b_2 = 4\)

For part (ii) \(b_1 = -2, b_2 = 5\)

10.
\[
\begin{cases}
-x_1 + 4x_2 + x_3 = b_1 \\
x_1 + 9x_2 - 2x_3 = b_2 \\
6x_1 + 4x_2 - 8x_3 = b_3
\end{cases}
\

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