17. In R² (column vectors) show that (x, y) = x² Ay is an inner product where 3 A = ¹- (³7) -- (-)). - (1) = . y = 1 X2 What is the corresponding norm ||™||?
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- Show that the functions x and x2 are orthogonal in P5 with inner product defined by (5), where xi = (i − 3)/2 for i = 1, . . . , 5.19. Show that there are infinitely many vectors in R# with Euclidean norm 1 whose Euclidean inner product with (1, −2,4) is zero.If Z1, Z2, Z3 are independent and identically distributed, such that Zi--Geom(0.4) for i=1,2,3. What is P(Z1+Z2+Z3=7)?
- If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:Recall that we say that a random variable X is in the vector space L^2 if it has finite second moment, EX^2 In this problem we will understand a bit better the geometry of the vector space L^2(1) Show that ||X||_2 = √EX^2 is a normEvaluate the work done between point 1 and point 2 for the conservative field F.F = 6x i + 6y j + 6z k; P 1(4, 3, 5) , P 2(5, 6, 7) a)W = 180 b) W = 480 c) W = 0 d) W = - 180
- 1. Determine the exact distance between the planes 4 x + y – 2 z + 10 = 0 and 8 x + 2 y – 4 z – 12 = 0 . no matrix grade 12 knowloge onlyThe vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain, in general?)Suppose A is a 2x2 invertible Martix. Is the following statement true or false? For each vector b, which is an element of R^2, there is one and only one vector x, which in an element of R^2, such that A*vector x=vector b.