Chapter 2.4, Problem 1P

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

$V=\{[101],[121],[222]\}$

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

$A=\left[\begin{array}{l}101\\ 121\\ 222\end{array}\right]$

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

Exchange row 3 and row 1, then the following matrix is obtained,

$\left[\begin{array}{l}222\\ 121\\ 101\end{array}\right]$

Multiply row 1 with 0.5, then the following matrix is obtained,

$\left[\begin{array}{l}111\\ 121\\ 101\end{array}\right]$

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

$[\begin{array}{l}111\\ 0\end{array}$