# linearly dependent set of three vectors

What is an example of a linearly dependent set of three vectors with the property that any single vector can be removed from the set without changing the span of the set?

What is an example of a linearly dependent set of three vectors that does not have the property as Question above?

© BrainMass Inc. brainmass.com October 17, 2018, 12:41 am ad1c9bdddfhttps://brainmass.com/math/vector-calculus/linearly-dependent-set-three-vectors-305347

#### Solution Preview

1) What is an example of a linearly dependent set of three vectors with the property that any single vector can be removed from the set without changing the span of the set?

Here is an example (we can only consider 3-dimensional vectors):

u=(1, 2, 3); ...

#### Solution Summary

A linearly dependent set of three vectors is examined.

Minimal linearly dependent sets of columns

Given two matrices

{1 2 3 3 9

1 0 1 0 2

0 2 2 3 7

2 4 6 6 18}

{9 3 9 3

9 1 3 3

9 0 2 5

6 0 0 2

3 1 3 1}

for each one:

a) list all minimal linearly dependent sets of columns;

b) list all maximal linearly independent sets of columns;

c) list all minimal sets of columns which span all columns; a',b',c') The same for rows;

d) compute the rank.