Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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F1.6 Question 15 on paper please
![### Linear Systems and Matrix Equations
**11. Solve the following systems of linear equations.**
\[
\begin{aligned}
i. \quad x_1 + 2x_2 &= b_2 \\
x_1 + 2x_2 + b_2 &= 1 \\
b_1 &= 0, \quad b_2 = 1
\end{aligned}
\]
\[
\begin{aligned}
ii. \quad b_1 &= -4, \quad b_2 = 6
\end{aligned}
\]
\[
\begin{aligned}
iii. \quad b_1 &= -1, \quad b_2 = 3
\end{aligned}
\]
\[
\begin{aligned}
iv. \quad b_1 &= -5, \quad b_2 = 1
\end{aligned}
\]
**12. In Exercises 13–17, determine conditions on the \(b_i\)'s, if any, in order to guarantee that the linear system is consistent.**
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 &= b_1 \\
-x_1 - 2x_2 &= b_2 \\
-2x_1 + 5x_2 + 4x_3 &= b_3
\end{aligned}
\]
\[
\begin{aligned}
i. \quad b_1 &= 1, \quad b_2 = 0, \quad b_3 = -1
\end{aligned}
\]
\[
\begin{aligned}
ii. \quad b_1 &= 1, \quad b_2 = 0, \quad b_3 = 1
\end{aligned}
\]
\[
\begin{aligned}
iii. \quad b_1 &= -1, \quad b_2 = -1, \quad b_3 = 0
\end{aligned}
\]
**13.**
\[
\begin{aligned}
x_1 + 3x_2&= b_1 \\
-2x_1 + x_2&= b_2
\end{aligned}
\]
**14.**
\[
\begin{aligned}
6x_1 - 4x_2 &= b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccdd90b5-cd41-4340-8a36-15b102c9ba73%2Fdf842605-a0e0-4a28-a5ce-124fce7405e5%2Ft1ov268_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Systems and Matrix Equations
**11. Solve the following systems of linear equations.**
\[
\begin{aligned}
i. \quad x_1 + 2x_2 &= b_2 \\
x_1 + 2x_2 + b_2 &= 1 \\
b_1 &= 0, \quad b_2 = 1
\end{aligned}
\]
\[
\begin{aligned}
ii. \quad b_1 &= -4, \quad b_2 = 6
\end{aligned}
\]
\[
\begin{aligned}
iii. \quad b_1 &= -1, \quad b_2 = 3
\end{aligned}
\]
\[
\begin{aligned}
iv. \quad b_1 &= -5, \quad b_2 = 1
\end{aligned}
\]
**12. In Exercises 13–17, determine conditions on the \(b_i\)'s, if any, in order to guarantee that the linear system is consistent.**
\[
\begin{aligned}
x_1 + 3x_2 + 5x_3 &= b_1 \\
-x_1 - 2x_2 &= b_2 \\
-2x_1 + 5x_2 + 4x_3 &= b_3
\end{aligned}
\]
\[
\begin{aligned}
i. \quad b_1 &= 1, \quad b_2 = 0, \quad b_3 = -1
\end{aligned}
\]
\[
\begin{aligned}
ii. \quad b_1 &= 1, \quad b_2 = 0, \quad b_3 = 1
\end{aligned}
\]
\[
\begin{aligned}
iii. \quad b_1 &= -1, \quad b_2 = -1, \quad b_3 = 0
\end{aligned}
\]
**13.**
\[
\begin{aligned}
x_1 + 3x_2&= b_1 \\
-2x_1 + x_2&= b_2
\end{aligned}
\]
**14.**
\[
\begin{aligned}
6x_1 - 4x_2 &= b
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