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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.
Solve the following.
Exponential equation by isolating the natural logarithm.
Power Notebooks plans to manufacture a new line of notebook computers. The screens cost $100 each. To set up assembly process required to produce screens in house would cost $100,000.
To find a number which tells what person in a row (if no more than 9 people are in a row) is wearing a ring on which joint of which finger, double the number of the person in the row
Define a polynomial and a rational expression. What makes a rational expression unique? Provide two original examples of a rational expression and two that are not. Mix the expressions up and label them A. B. C. and D..
Apply the order of operations to solve.
Three different quadratic functions.
Find a three-digit positive integers such that the sum of all three digit is 14, the tens digit is two more than ones and if the digit is reversed, the number is unchanged.
To estimate gorilla populations, biologists count the total number of gorillas in a small section of their habitat. The total population of gorillas is directly proportional to the size of the habitat (in acres) polled.
In the following examples, determine whether the subset W ⊆ V is a subspace: (a) V = F(R,R) is the R-vector space of all functions from R to R and W = {f : R → R | f (3) =-2} is the subset consisting of those functions f : R → R such that f (3) = -2..
5x-y+9, 2x-2y+7, what is the solution?
computer crime has become a serious matter for your discussion board post consider the followingdo you think computer
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