# vectors

18:15 1 …4G く返回 222_HW_09.pdf Q MATH 222 HOMEWORK #09 Problem 1 Carry out the Gram-Schmidt process on these sets of vectors a) {(1,0,2,4,5), (1,4,3,2, 6)} b) {(1,0,1),(3,1,3), (5,-3,3)} Problem 2 For each of the given bases, express (1,1,1) as a linear combination of the basis vector’s. a) {(1,1,0),(0,1,1),(1,0,1) b) {(1,-1,-1), (0, 1, -1), (2,1,1)} c) {1/85, -1/78, -1/33), (0.4/12, -1/12), (2/5,1/5, 1/78)} Problem 3 Show that the following is an inner product on R’. ((41, 42, 43), (W1, W2, w3)) = 4141 +21202 + 3u3w3 Problem 4 Show that the following is not an inner product on R. ((uz, uy, u3), (wy, wz, wy)) = xw1 + Uw9 Problem 5 Consider the inner product (5,9) == “s(a)g(e) dr. a) Calculate (2, cos(2.c)). b) Calculate || 231. c) Show that (sin(x), cos(x)} is an orthonormal set. 9 81 DOO ODO 控制面板 日历 待办事项 通知 收件箱

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