### Question 10**Problem Statement:**Describe all solutions of \( \mathbf{A}\mathbf{x} = \mathbf{0} \) in parametric vector form, where:\[ \mathbf{A} = \begin{bmatrix} 1 & 5 & 2 & -6 & 9 & 0 \\ 0 & 1 & -7 & 4 & -8 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}\]**Choices:**1. \[ \mathbf{x} = x_2 \begin{bmatrix} -5 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix} + x_4 \begin{bmatrix} -8 \\ 0 \\ 7 \\ 1 \\ 0 \\ 0 \end{bmatrix} + x_5 \begin{bmatrix} -1 \\ 0 \\ -4 \\ 0 \\ 1 \\ 0 \end{bmatrix} \]2. \[ \mathbf{x} = x_2 \begin{bmatrix} 5 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix} + x_4 \begin{bmatrix} -8 \\ 0 \\ 7 \\ 1 \\ 0 \\ 0 \end{bmatrix} + x_5 \begin{bmatrix} -1 \\ 0 \\ -4 \\ 0 \\ 1 \\ 0 \end{bmatrix} \]3. \[ \mathbf{x} = x_2 \begin{bmatrix} -5 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix} + x_4 \begin{bmatrix} -8 \\ 0 \\ 7 \\ 1 \\ 0 \\ 0 \end{bmatrix} + x_5 \begin{bmatrix} -1 \\ 0 \\ -4 \\ 0 \\ 1 \\ 0 \end{bmatrix} \]4. \[ \mathbf{x} = **Linear Algebra: Finding Non-Trivial Solutions****Problem Statement:**Find a non-trivial solution of the equation \( A \mathbf{x} = \mathbf{0} \), where \( A = \begin{bmatrix}-15 & -3 \\30 & 6 \\-10 & -2\end{bmatrix} \).**Options:**1. \(\mathbf{x} = \begin{bmatrix}0 \\0\end{bmatrix}\)2. \(\mathbf{x} = \begin{bmatrix}-5 \\1\end{bmatrix}\)3. \(\mathbf{x} = \begin{bmatrix}5 \\-1\end{bmatrix}\)4. \(\mathbf{x} = \begin{bmatrix}1 \\-5\end{bmatrix}\)5. \(\mathbf{x} = \begin{bmatrix}-1 \\5\end{bmatrix}\)**Explanation:**In this problem, we are given a matrix \( A \) and we need to find a non-trivial solution \(\mathbf{x}\) such that \( A \mathbf{x} = \mathbf{0} \). A non-trivial solution is a solution where \(\mathbf{x} \neq \mathbf{0} \).You are required to find the correct \(\mathbf{x}\) vector from the given options that satisfies this equation.

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Question 10 152 0 0 1 Describe all solutions of Ax = 0 in parametric vector form, where A = 0 0 0 0 7 x = 4₂ O x = 2₂ x = 2₂ 5 0 0 0 51 1 0 0 0 5 1 0 0 + IL + 14 +14 201 7 1 0 8 0 7 1 0 0 7 1 + as + Is + 15 + IS ToTomo -4 1 0 -4 0 0 4 0 0 0 -6 9 0 -74 -8 0 0 1 0 0 0

Question 10 152 0 0 1 Describe all solutions of Ax = 0 in parametric vector form, where A = 0 0 0 0 7 x = 4₂ O x = 2₂ x = 2₂ 5 0 0 0 51 1 0 0 0 5 1 0 0 + IL + 14 +14 201 7 1 0 8 0 7 1 0 0 7 1 + as + Is + 15 + IS ToTomo -4 1 0 -4 0 0 4 0 0 0 -6 9 0 -74 -8 0 0 1 0 0 0

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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Question

**Linear Algebra: Finding Non-Trivial Solutions**

**Problem Statement:**
Find a non-trivial solution of the equation \( A \mathbf{x} = \mathbf{0} \), where \( A = \begin{bmatrix}
-15 & -3 \\
30 & 6 \\
-10 & -2
\end{bmatrix} \).

**Options:**

1. \(\mathbf{x} = \begin{bmatrix}
0 \\
0
\end{bmatrix}\)

2. \(\mathbf{x} = \begin{bmatrix}
-5 \\
1
\end{bmatrix}\)

3. \(\mathbf{x} = \begin{bmatrix}
5 \\
-1
\end{bmatrix}\)

4. \(\mathbf{x} = \begin{bmatrix}
1 \\
-5
\end{bmatrix}\)

5. \(\mathbf{x} = \begin{bmatrix}
-1 \\
5
\end{bmatrix}\)

**Explanation:**

In this problem, we are given a matrix \( A \) and we need to find a non-trivial solution \(\mathbf{x}\) such that \( A \mathbf{x} = \mathbf{0} \). A non-trivial solution is a solution where \(\mathbf{x} \neq \mathbf{0} \).

You are required to find the correct \(\mathbf{x}\) vector from the given options that satisfies this equation.

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1. Solve the following vector equations, put your answers in parametric vector form, then compare your work and answers. 3 2 7 (a) 1 4 -1|0 3 2 7 14 (b) | 1 4 -1 8 3 2 7 -3 (c) 14 -1 9.

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Advanced Engineering Mathematics

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ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated