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Given a vector w, the inner product of R^n is defined by:<x,y>=Summation from i=1 to n (xi,yi,wi)
[a] Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T
Show that x and y are orthogonal with respect to this inner product. Compute the values of ||x|| and ||y|| with respect to this inner product.
[b]In C[0,1], with inner product defined above, consider the vectors 1 and x. Find the angle theta between 1 and x. Determine the vector projection p of 1 onto x and verify that 1-p is orthogonal to p.
identify the slope and y-intercept of the line whose equation is given 15x 2y 12 25y -25 35x - y
1. use the midpoint formula. find the midpoint between the following points.a14 and b56.a4 6 and b-2 -2a3 -4 and b5
What is the significance of the name 'linear equation' to its graphical representation?
Find an irreducible monic polynomial of degree 2 over the field Z_7 whose root is a primitive element GF(49).
Plot the points and determine the slope of the line containing them. Graph Line. (-3,-7) (2,-7). For the intercepts and use them to graph equation 6x+2y=12.
How can we picture real numbers "mod 2 pi" as something that goes round in a ring? How is that related to trigonometry? Can we make a function from "real numbers mod 2 pi" to the rotations around the origin of the Cartesian plan so that this functi..
Graph y^2=x^2 and explain why the graph is not a function. Determine the period and amplitude of the function y=sin 6x then graph it.
Choose three integers a, b, and c. (Negative numbers are welcome.) Now use a, b, and c to create a trinomial ax2+bx+c. Can you factor this trinomial? How would you create a trinomial that will factor?
Type exponential notation with positive exponents
Consider the map Φ : (Z, +) →(Zn, + (mod n)) given by Φ(t) ≡ t (mod n). State the first isomorphism theorem and apply it to the map Φ
Write the equation in the slope-intercept form. Find the domain and range of the relation, and state whether or not the relation is a function.
Write a summary on "who I am " about his self. summary about myself. I need your to know do have a any suggestion or examples?
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