Exercise Set 1.6 In Exercises 1-8, solve the system by inverting the coefficient matrix and using Theorem 1.6.2. 1. x₁ + x₂ = 2 5x₁ + 6x₂ = 9 2. 4x₁3x₂ = -3 2x₁ - 5x₂ = 9 3. x₁ + 3x₂ + x3 = 4 4. 5x₁ + 3x₂ + 2x3 = 4 3x₁ + 3x₂ + 2x3 = 2 2x₁ + 2x₂ + x3 = -1 2x₁ + 3x₂ + x3 = 3 x₂ + x3 = 5 6. - x + y + z = 5 x-2y3z=0 x+y=4z = 10 -4x + y + z = 0 w + x + 4y + 4z = 7 w + 3x + 7y +9z = 4 -w- 2x - 4y - 6z = 6 5.
Exercise Set 1.6 In Exercises 1-8, solve the system by inverting the coefficient matrix and using Theorem 1.6.2. 1. x₁ + x₂ = 2 5x₁ + 6x₂ = 9 2. 4x₁3x₂ = -3 2x₁ - 5x₂ = 9 3. x₁ + 3x₂ + x3 = 4 4. 5x₁ + 3x₂ + 2x3 = 4 3x₁ + 3x₂ + 2x3 = 2 2x₁ + 2x₂ + x3 = -1 2x₁ + 3x₂ + x3 = 3 x₂ + x3 = 5 6. - x + y + z = 5 x-2y3z=0 x+y=4z = 10 -4x + y + z = 0 w + x + 4y + 4z = 7 w + 3x + 7y +9z = 4 -w- 2x - 4y - 6z = 6 5.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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F1.6 Question 1 part 1 and 5 please on paper
![# Exercise Set 1.6
## Instructions:
In Exercises 1–8, solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
### Problems:
1.
\[
\begin{cases}
x_1 + x_2 = 2 \\
5x_1 + 6x_2 = 9
\end{cases}
\]
2.
\[
\begin{cases}
4x_1 - 3x_2 = -3 \\
2x_1 - 5x_2 = 9
\end{cases}
\]
3.
\[
\begin{cases}
x_1 + 3x_2 + x_3 = 4 \\
2x_1 + 2x_2 + x_3 = -1 \\
2x_1 + 3x_2 + x_3 = 3
\end{cases}
\]
4.
\[
\begin{cases}
5x_1 + 3x_2 + 2x_3 = 4 \\
3x_1 + 3x_2 + 2x_3 = 2
\end{cases}
\]
5.
\[
\begin{cases}
x + y + z = 5 \\
x + y - 4z = 10 \\
-4x + y + z = 0
\end{cases}
\]
6.
\[
\begin{cases}
-x - 2y - 3z = 0 \\
w + x + 4y + 4z = 7 \\
w + 3x + 7y + 9z = 4 \\
-w - 2x - 4y - 6z = 6
\end{cases}
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Transcribed Image Text:# Exercise Set 1.6
## Instructions:
In Exercises 1–8, solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
### Problems:
1.
\[
\begin{cases}
x_1 + x_2 = 2 \\
5x_1 + 6x_2 = 9
\end{cases}
\]
2.
\[
\begin{cases}
4x_1 - 3x_2 = -3 \\
2x_1 - 5x_2 = 9
\end{cases}
\]
3.
\[
\begin{cases}
x_1 + 3x_2 + x_3 = 4 \\
2x_1 + 2x_2 + x_3 = -1 \\
2x_1 + 3x_2 + x_3 = 3
\end{cases}
\]
4.
\[
\begin{cases}
5x_1 + 3x_2 + 2x_3 = 4 \\
3x_1 + 3x_2 + 2x_3 = 2
\end{cases}
\]
5.
\[
\begin{cases}
x + y + z = 5 \\
x + y - 4z = 10 \\
-4x + y + z = 0
\end{cases}
\]
6.
\[
\begin{cases}
-x - 2y - 3z = 0 \\
w + x + 4y + 4z = 7 \\
w + 3x + 7y + 9z = 4 \\
-w - 2x - 4y - 6z = 6
\end{cases}
\]
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