Question

HAPPY BELATED LINEAR INDEPENDENCE DAY!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

why linear?

Answer 2

Let the set {v1,v2} be linearly independent in a vector space V. Show that if a vector v3 is not of the form av1 + bv2, then the set {v1,v2,v3} is linearly independent.

Answer 3

ha

Answer 4

for the set of vectors to be linearly independent means:
\(av_1+bv_2+cv_3=0\) is satisfied only if a,b,c are all equal to 0.
To get to this from what you have, supose it's not true, supose c \(\neq\) 0 and write it in this way:
\(-(a/c)v_1-(b/c)v_2=v_3\)
but this contradicts the asumption that \(v_3\) has not his type of expretion \(av_1 + bv_2\)

Answer 5

hope it helps