Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![### Problem 1
**Question:**
For which value(s) of \( k \) does the system
\[
\begin{align*}
x_1 + x_2 - x_3 &= -2 \\
3x_1 - 5x_2 + 13x_3 &= 18 \\
x_1 - 2x_2 + 5x_3 &= k
\end{align*}
\]
have no solution.
**Answer:**
1. _______
---
### Problem 2
**Question 1:**
(True/False) There is a sequence of elementary row operations that transforms the matrix
\[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\]
into
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
**Answer:**
1. ________
---
**Question 2:**
(True/False) Vector
\[
\begin{bmatrix}
1 \\
2 \\
3
\end{bmatrix}
\]
is a linear combination of the vectors
\[
\begin{bmatrix}
4 \\
5 \\
6
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
7 \\
8 \\
9
\end{bmatrix}
\]
**Answer:**
2. ________](https://content.bartleby.com/qna-images/question/8cf9958e-dd38-41eb-b691-55a1e2252bf8/d59839ee-6a63-485e-bcdf-f3e2e7bb3f77/ho7hsvg_processed.jpeg)
Transcribed Image Text:### Problem 1
**Question:**
For which value(s) of \( k \) does the system
\[
\begin{align*}
x_1 + x_2 - x_3 &= -2 \\
3x_1 - 5x_2 + 13x_3 &= 18 \\
x_1 - 2x_2 + 5x_3 &= k
\end{align*}
\]
have no solution.
**Answer:**
1. _______
---
### Problem 2
**Question 1:**
(True/False) There is a sequence of elementary row operations that transforms the matrix
\[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\]
into
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
**Answer:**
1. ________
---
**Question 2:**
(True/False) Vector
\[
\begin{bmatrix}
1 \\
2 \\
3
\end{bmatrix}
\]
is a linear combination of the vectors
\[
\begin{bmatrix}
4 \\
5 \\
6
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
7 \\
8 \\
9
\end{bmatrix}
\]
**Answer:**
2. ________
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