1)(For what values of k, if any, is the vector (k2,−3k,−2) ∈R3 in the span of {(1,2,3),(0,1,1),(1,3,4)}?
2) Let
be given.
(aFind the reduced echelon form of A.
(b)Find a basis for the Row(A).
(c)Find a basis for the Col(A).
(d) Find a basis for the Null(A).
(e) What are the rank and nullity of A?
3) Let W be a subspace of R5 is spanned by the vectors v1 = (1,3,−1,2,3), v2 = (2,7,−2,5,2), v3 = (1,4,−1,3,−1)
(a) Find a basis for W . What is the dim(W)?
(b) Find a basis for the orthogonal complement W⊥ of W. What is the dim(W⊥) ?
