2/7 -1/5 4/13 3/2 1/8 3/35 47/26 37/8 100/33 A = 9/2 | 4/11 8/3 The matrix above has the property the sum of the first two columns is equal to the third column (you don't have to check that yourself.) Use this fact to find a nontrivial solution to Ax = 0.

2/7 -1/5 4/13 3/2 1/8 3/35 47/26 37/8 100/33 A = 9/2 | 4/11 8/3 The matrix above has the property the sum of the first two columns is equal to the third column (you don't have to check that yourself.) Use this fact to find a nontrivial solution to Ax = 0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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Question

2/7
-1/5
3/2
1/8
8/3
3/35
47/26
37/8
100/33
4/13
A =
9/2
4/11
The matrix above has the property the sum of the first two columns is equal to the third column
(you don't have to check that yourself.) Use this fact to find a nontrivial solution to Ax = 0.

Expert Solution

Step 1

Given matrix is $A = [\begin{matrix} \frac{2}{7} & - \frac{1}{5} & \frac{3}{35} \\ \frac{4}{13} & \frac{3}{2} & \frac{47}{26} \\ \frac{9}{2} & \frac{1}{8} & \frac{37}{8} \\ \frac{4}{11} & \frac{8}{3} & \frac{100}{33} \end{matrix}]$

Given system is $A x = 0 . . . . . (1)$

$[\begin{matrix} \frac{2}{7} & - \frac{1}{5} & \frac{3}{35} \\ \frac{4}{13} & \frac{3}{2} & \frac{47}{26} \\ \frac{9}{2} & \frac{1}{8} & \frac{37}{8} \\ \frac{4}{11} & \frac{8}{3} & \frac{100}{33} \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ 0 \\ 0 \end{matrix}]$

Now, write the augmented matrix $(A | 0)$

$(A | 0) = [\begin{matrix} \frac{2}{7} & - \frac{1}{5} & \frac{3}{35} & 0 \\ \frac{4}{13} & \frac{3}{2} & \frac{47}{26} & 0 \\ \frac{9}{2} & \frac{1}{8} & \frac{37}{8} & 0 \\ \frac{4}{11} & \frac{8}{3} & \frac{100}{33} & 0 \end{matrix}]$

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