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A function T:V→W between vector spaces V and W is called additive if T(x + y) = T(x) + T(y) for all x, y ∈V. Prove that if V and W are vector spaces over the field of rational numbers, then any additive function from V into W is a linear transformation.
My attempt to prove this would be to show that T(x) is closed under scalar multiplication because by definition then T would be linear, but I am not sure how to show this.
The number of green balls is 1 more than 1/3 the number of blue balls. In total, she has 15 balls. An equation created to find the number of blue balls will have one solution , no solution, or infinitely solutions.
Two thousand tickets to the raffle are to be sold at $1 apiece. If a person purchases four tickets, what will be the expected value of the tickets?
Find an equation for the parabola that has its vertex at the origin and satisfies the given condition.
Find the work done by the force field F(x,y,z) = / (x^2+y^2+z^2)^(3/2)
Age of drivers in crash fatalities the number of crash fatalities per 100,000 vehicle miles of travel (based on 1994 data) is approximated by the model
A fitness ball is delivered in a flat package witha hand pump. The pump inflates the ball at a rate of 280 cmcubed per pump, to a diameter of 28cm. How many pumps are needed to inflate the ball? Please explain how you got it.
Matrix of transition probabilities. The daily price of a farm commodity is up, down, or unchanged from the day before. Analysts predict that if the last price was down, there is a .5 probability the next will be down,
In each of the following parts, you should simplify your answers where it is appropriate to do so. Write down the derivative of each of the functions
the bottom of a storage tank at a rate of r(t) = 200-4t liters per minute, where 0≤ t ≤ 66. Find the amount of water that flows from the tank during the first 66 minutes.
Car A and Car B leave the origin at noon. Car A travels north at 33 mph and car B travels east at 56 mph.
Tropical pools figures that its monthly revenue on the sale of ‘x' pools is given by R = 1500x - 3x2 where ‘x' is less than 25.
A planet follows an elliptical path described by 16x^(2)+4y^(2)=64. A comet follows the parabolic path y=x^(2)-4. Where might the comet intersect the orbiting planet?
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