b.) Let .3 = 3 Evaluate 0 ||2x+3y. (3 Marks) c) Given that x and y are orthogonal vectors, Simplify the expression (x+2y) (3x-2y.) (3 Marks) d.) Define linear depence. Show that the vectors 12 25 are linearly dependent. And show clearly how one of the vectors is a linear combination of the vectors. (4marks) e.) Let VR2. Show that I -2y= is a vector space of R. (3 Marks) f.) Show that the set S={(1, 1), (3,4)) is a basis for R. (2 Marks) g.) Suppose that the set S {} is a basis for the vector space V, then show that every vector space space from V can be expressed as a linear combination of the vectors from S in exactly one way. (3 Marks) h.) For each of the following systems, Write down the augmented form of the system but DO NOT solve the system. 1)x+y+2=6 2x-y+=3 3 -0 (1 Mark) 1)+y+z+w=6 2x+3y w 0 -3x+4y++2=4 z+w=0 x+2y (2 Marks) 1.) Determine the dimension of subspace R below (6 Marks) 1) w ={(x,y,0,y R} is a vector space of R 1.) w = {(x, xy, yr, yR} s a vector space of Rs. iii.) W3= {(x, y, 12x+yER} is a vector space of R