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Which of the following sets are linear spaces?
a) {X = (x1, x2, x3) in R3 with the property x1 - 2x3 = 0}
b) The set of solutions x of Ax = 0, where A is an m × n matrix.
c) The set of 2 × 2 matrices A with det(A) = 0.
d) The set of polynomials p(x) with R1 -1 p(x) dx = 0. e) The set of solutions y = y(t) of y'' + 4y' + y = 0.
an automobile purchased for $24,000 is worth $2,300 after seven years. Assuming the car's value depreciated steadily from year to year, what was it worth at the end of the third year.
Morris Leste, owner of Carlson Company, has three employees who earn $431, $503, and $738 per week. What are the total state and federal unemployment taxes that Morris owes for the first 12 weeks of the year and for week 30?
One boat travelling 15 mph goes 47 miles downstream in the same amount of time that another boat going 20 mph goes 40 miles upstream. How fast is the current in mph?
Find the points of inflection and discuss the concavity of the graph of the function f(x)=(x-2)^3(x-1).
Write an equation that can be used to determine the total weight of all the newspapers Sam has bundled.
Show the similarities between dividing two fractions and dividing two rational expressions using examples of each; Explain your steps.
The electricity costs of a business increased from $15,000 one year and $16,000 the next. To the nearest whole percent, what was the rate increase?
There are 10 workers and 2 administrators in a company meeting room. Two people will be selected at random without replacement. The chance that the second person is a worker is:
A rectangular piece of metal is 10 cm longer than it is wide. Squares with sides 2 cm long are cut from the four corners of the piece of metal, and the flaps are folded upward to form an open box. If the volume of the box is 832 cm3, what were the..
In this module's discussion, find the slope of an object either where you live, where you work, or outside somewhere. Examples might include a ladder positioned against a wall or against a house, a banister on a set of stairs, a slide in a park, e..
Translate this verbal sentence into a mathematical sentence: The difference between six and twice a number is 4 more than the number.
Let M>0, and let f:[a,b]-->R be a function which is continuous on [a,b] and differentiable on (a,b), and such that |f'(x)|
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