Chapter 2, Problem 13RP

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

$V=\{[121],[200]\}$

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

$A=\left[\begin{array}{l}121\\ 200\end{array}\right]$

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,

$\left[\begin{array}{l}121\\ 0-4-2\end{array}\right]$

Now, replace row 2 by ($-\frac{1}{4}(row2)$), then the following matrix is obtained,

$[\begin{array}{l}\mathrm{1<}\end{array}$