Reference no: EM131382041
1. Suppose x1, x2, x3 are linearly independent vectors in a vector space V and let
y1=x1+x2+x3
y2=x1+ax2
y3=x2+bx3
Find the conditions that must be satisfied by a and b to ensure that the vectors y1, y2, y3 are linearly independent.
2. Let w1,...,wj be vectors in a vector V and let vi ∈span{w1,...,wj} for all i=1,2,...,k.
Find an example to show that it is not true that span{v1,...,vk} = span{w1,...,wj}.
Under what conditions would span{v1,...,vk} = span{w1,...,wj}?
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