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Question: Use Cauchy's Inequality to show that
||u + v|| ≤ ||u|| + ||v||;
This is called the triangle inequality.
A careful examination of the proof just presented shows that we did not explicitly use the definition of the complex vector dot product, but only some of its properties. This suggested to mathematicians the possibility of abstracting these properties and using them to define a more general concept, an inner product, between objects more general than complex vectors, such as infinite sequences, random variables, and matrices. Such an inner product can then be used to define the norm of these objects and thereby a distance between such objects. Once we have an inner product defined, we also have available the notions of orthogonality and best approximation. We shall address all of these topics shortly.
Three particlesof mass 6kg,3kg and 2.5kg are attached to a light rod PR of length 3 meters at the point PQR where PQ=0.9 M .Find the position of the center of the system
Using the various properties Closure, Commutative etc. and Distributive, explain how you would compute the following, using quick and easy methods of association such as in 7+3 =10, 5'9=10 etc. and show the steps of your process.
Calculate the amount of interest paid for each option
Use the dual simplex method to solve the following LP:
How many license plates using 6 digits can the state of Vermont issue if repetition of digits is permitted - how many ways can the horses finish the race - How many of the first 100 natural numbers are multiples of 2 or multiples of 5?
Two investments are made totaling $8800. For a certain year these investments yielded $1326 in simple interest. Part of the $8800 was invested at 14% the part at 16%. Find the amount invested at each rate.
S List and count the number of possible combinations of objects from three sets, e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?
Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and a standard deviation 2 grams. Quality control inspectors randomly select 16 parts, weigh each,..
The first kernel pops 128 seconds after the microwave oven is started. What is the z-score of this kernel? Round your answer to two decimal places.
Determine the width of a river that flows due east if a surveyor finds that a tree on the opposite bank has a bearing of N 22°30' E from a certain point A and a bearing of N 15° W from another point B which is 400 feet downstream from A.
Pool tables are rectangular, and their length is twice the width. Find the dimensions of a pool table if it occupies 18 ft2 of floor space.
Recognize the importance of some very famous numbers, as well as learn more about approximations - Provide a short definition of Pi.
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