Question 4: a) b) i) ) ) i) ii) iv) Define what is meant by saying that a vector is a linear combination of vectors wq,Ws,...,W, in a vector space V. Determine if v= (2,-5,-1) is a linear combination of w1=(1,-2,1) and w>=(0,1,3)? Define the terms linearly independent and linearly dependent for a set of vectors {v1,v2,vs,...,Vn} Determine whether or not the set of vectors {(1,0,0,2),(2,2,0,0),(1,1,0,-1)} are linearly independent R* Define the terms basis and dimension for a vector space V. Find a basis of the subspace U= { x=(x1,x2,x3,x4) in R*: x4+ x2=xs} Prove your set is a basis What is the dimension of U? Question 5: Find an orthonormal basis for W = Span {x1, x2, x3} using Gram-Schmidt (you might wait until the very end to normalize all vectors at once): 0 0 0 1 X1 = 1 X2 = 1 1 X3 = 1 2 b (1 Mark) (3 Marks) (1 Mark) (3 Marks) (1 Mark) (3 Marks) (4 Marks) (3 Marks) (10 Marks)