Let S = {(x, y)|x, y R}. Suppose the vector addition and scalar multiplication in S are defined the same way as in R². L

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Let S X Y X Y R Suppose The Vector Addition And Scalar Multiplication In S Are Defined The Same Way As In R L 1 (45.54 KiB) Viewed 9 times

Let S = {(x, y)|x, y R}. Suppose the vector addition and scalar multiplication in S are defined the same way as in R². Let u = (₁, 2), V = (v₁, v₂) be vectors in S. We define an inner product in S according to the formula (u, v)=20₁₁-₁U₂ - V₂U₁ + V₂U₂. Show that S equipped with this inner product is a real inner product space. Let u = (1,3) and v = (2,1). i. Show that u and v form an orthogonal basis in the inner product space S defined in part b). Use this basis to find an orthonormal basis by normalizing each vector. (3 marks) ii. Use the inner product defined in part b) to express the vector w = (1, 1) as a linear combination of the orthonormal basis vectors obtained in part i. (4 marks) (2 marks)