Chapter 2.4, Problem 6P

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

$V=\left\{\left[\begin{array}{l}1\\ 0\\ 0\end{array}\right]\left[\begin{array}{l}0\\ 2\\ 1\end{array}\right]\left[\begin{array}{l}1\\ 0\\ 1\end{array}\right]\right\}$

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

$A=\left[\begin{array}{l}101\\ 020\\ 011\end{array}\right]$

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

Replace row 2 by ($\frac{1}{2}(row2)$), then the following matrix is obtained,

$[\begin{array}{l}101\\ 010\\ 011\end{array}$