Chapter 2.4, Problem 2P

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

$V=\{[210],[120],[331]\}$

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

$A=\left[\begin{array}{l}210\\ 120\\ 331\end{array}\right]$

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

Replace row 1 by ($\frac{1}{2}(row1)$), then the following matrix is obtained,

$\left[\begin{array}{l}1\frac{1}{2}0\\ 120\\ 331\end{array}\right]$

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

$\left[\begin{array}{l}1\frac{1}{2}0\\ 0\frac{3}{2}0\\ 331\end{array}\right]$

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

$\left[\begin{array}{l}1\frac{1}{2}0\\ 0\frac{3}{2}0\\ 0\frac{3}{2}1\end{array}\right]$