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Linear Combinations, Basis and Transformations
1. Given a basis B = { u1 = [1, 2], u2 = [2, 1] } for R^2, express u = [7, -2] as a linear combination of u1 and u2. How many ways can you do this? (in this problem...the u1 and u2 should actually be u sub 1 and u sub 2...I couldn't do that notation here....also the u1, u2, and u should all be bold to represent vectors)
2. Let T be the reflection through the x - axis in R^2. Is T a linear transformation? If so, find the standard matrix of T.
Probability questions with cards and unbiased dice, Suppose that you select two cards without replacement from an ordinary deck of playing cards.
Prove that f(x) is continuous at every irrational point and discontinuous at every rational point. Show that f is integrable on [0,1]
Suppose I had a lemonade stand. When I charge $1, I sold 50 cups, when I raised the price to $2, I only sold 25 cups. Write an equation for the number of cups I sold as a function of the price i charged.
From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns.
Important information about Probability and combinations. Assume you have five cards are chosen from a standard deck of 52 playings cards. How many hands contain four aces?
How many different passwords can be formed? b) How many different passwords have no repeated number or letters?
Estimate the galois group.
If Player A gets to throw 2 darts and Player B gets to throw 5 darts, how do you calculate the probability of Player A or Player B getting the highest total score?
The "origin" of cartesian plane in math is the point where x and y are both zero. Provided a variable, origin of type Point, a structured type with two fields, x and y, both of type double.
A bag contains 10 red, 12 green, and 8 yellow marbles. Assuming that all marbles are equally likely to be picked from the bag
Description of Joint probability, However in this problem what do I do with 2X in my upper y limit, can I plug in the max x value and just make it 0
Independent flips of a coin that lands on heads with probability p are made. What is the probability that the first four outcomes are
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