In each of the following examples decide if the vector forms

In each of the following examples decide if the vector forms a linearly independent set not. If they do not, then express one vector in the list as a linear combination of the others. V_1 = (4, -1, 1, 2) V_2 = (3, 2, 3, 1) V_3 = (2, 5, 5, 0) Which id any of the below sets of vector\'s spans a 4- dimensional space:

Solution

4a +3b+2c = 0

-a+2b+5c=0

a+3b+5c=0

Solving gives b = -2a and c = a

Now 2a +b = 0

4 dimensional spacesare spanned by 4 dimensional vectors and higher dimensions

so 1,3,4,5 span 4 dimensional spaces

so the vectors are linearly dependent..