[maria69]

I have finished all the parts of first question but i just don't know how to work in
(iv) part. i know that the answer should be :infinite number of possibilities, one answer is [-8;8;-1;0;1]. Can someone pleaseeeeeeee show me the solution??? pleaseee??
THank you very much maria!

[Yggdrasil]

To show

I have finished all the parts of first question but i just don't know how to work in
(iv) part. i know that the answer should be :infinite number of possibilities, one answer is [-8;8;-1;0;1]. Can someone pleaseeeeeeee show me the solution??? pleaseee??

You have an answer there.  To show that it can form a base with v₃ all you have to do is show that it is in S₂ and it is linearly independent with v₃.

[Martingale]

I have finished all the parts of first question but i just don't know how to work in
(iv) part. i know that the answer should be :infinite number of possibilities, one answer is [-8;8;-1;0;1]. Can someone pleaseeeeeeee show me the solution??? pleaseee??
THank you very much maria!

how about [-7,7,-1,1,0]

if you can do (ii) you should be able to do (iv)