Problem 1 Given the matrix A = 2. Solve AX=0 where -1 3 2 -6 2 4 2 3 -4 -1 9 -6-2-8 1 -1 12 1. Find the reduced row echelon form of A. Do not write every step, just the rref(A) is needed. Make sure it is correct. X=[T1 T2 73 74 25 26]T Bue 3. Write the solution in vector form and use it to find a basis for the solution space. Jani
Problem 1 Given the matrix A = 2. Solve AX=0 where -1 3 2 -6 2 4 2 3 -4 -1 9 -6-2-8 1 -1 12 1. Find the reduced row echelon form of A. Do not write every step, just the rref(A) is needed. Make sure it is correct. X=[T1 T2 73 74 25 26]T Bue 3. Write the solution in vector form and use it to find a basis for the solution space. Jani
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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![# Linear Algebra Problem Set
## Problem 1
Given the matrix
\[
A =
\begin{bmatrix}
-1 & 3 & 1 & 4 & 2 & 3 \\
2 & -6 & 2 & -4 & -1 & 9 \\
2 & -6 & -2 & -8 & 1 & -1
\end{bmatrix}
\]
1. Find the reduced row echelon form of \(A\). Do not write every step, just the rref(A) is needed. Make sure it is correct.
2. Solve \(AX = 0\) where
\[
X =
[x_1 \; x_2 \; x_3 \; x_4 \; x_5 \; x_6]^T
\]
3. Write the solution in vector form and use it to find a basis for the solution space.
4. Solve the following system and write the solution in vector form.
\[
AX =
\begin{bmatrix}
-2 \\
1 \\
0
\end{bmatrix}
\]
---
### Solution 1:
{% include solution format here if needed %}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe52e616-7bd7-4d85-a476-7e5fcec53ee5%2F55d906dd-d461-4dd0-a2fa-3ecb66084fde%2F6cqc3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Linear Algebra Problem Set
## Problem 1
Given the matrix
\[
A =
\begin{bmatrix}
-1 & 3 & 1 & 4 & 2 & 3 \\
2 & -6 & 2 & -4 & -1 & 9 \\
2 & -6 & -2 & -8 & 1 & -1
\end{bmatrix}
\]
1. Find the reduced row echelon form of \(A\). Do not write every step, just the rref(A) is needed. Make sure it is correct.
2. Solve \(AX = 0\) where
\[
X =
[x_1 \; x_2 \; x_3 \; x_4 \; x_5 \; x_6]^T
\]
3. Write the solution in vector form and use it to find a basis for the solution space.
4. Solve the following system and write the solution in vector form.
\[
AX =
\begin{bmatrix}
-2 \\
1 \\
0
\end{bmatrix}
\]
---
### Solution 1:
{% include solution format here if needed %}
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