Chapter 2.4, Problem 5P

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

$V=\left\{\left[\begin{array}{l}1\\ 2\\ 3\end{array}\right]\left[\begin{array}{l}4\\ 5\\ 6\end{array}\right]\left[\begin{array}{l}5\\ 7\\ 9\end{array}\right]\right\}$

A matrix A is formed as given below; whose rows are the above given vectors:

$A=\left[\begin{array}{l}145\\ 257\\ 369\end{array}\right]$

The Gauss-Jordan method is applied to find the dependency of the above given sets of vectors.

Replace row 2 by (row 2 – 2 (row 1)), then the following matrix is obtained,

$\left[\begin{array}{l}145\\ 0-3-3\\ 369\end{array}\right]$

Now, replace row 3 by (row 3 – 3 (row 1)), then the following matrix is obtained,

$[$