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Please provide an answer to the following questions below that contains 250 to 300 words each.
1. By looking at two linear equations, how can you tell that the corresponding lines are parallel, the same graph, or intersecting lines? How many solutions does each possibility have and why is that? Show examples for each possible situation.
2. Is there a difference between solving a system of equations by the algebraic method and the graphical method? Why? What are the advantages and disadvantages of each?
3. Write 250-300 words comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by appropriate examples.
Framing algebraic equations
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
Description of Probability : Random Selection, Suppose there are two vendors and each provides 50% of the items. The lifetime (in days) of an item from the first vendor is Exp
Increasing and decreasing intervals.
A difference between the mean number of volunteer hour
The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0
Multiple choice question from Probability and Set Language and valid probability distribution for a sample space
Statistics: Populations, Samples, Parameters and Assessing the Mean. The average time before hittin a jackpot at the local casino was estimated by using the average time that it took the first 100 players. Based on this information identify.
Digit probability A young girl gave a young man her phone number during a hurried parting. The young man remembers the 7 digits of her phone number
Calculating the probability from a given situation using combinations. A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random.
the dual degree students are receiving lower grades? Explain your answer to receive full credit.
A nontrivial graph G is called prime if G = G_1 x G_2 implies that G_1 or G_2 is trivial. Show that if a connected graph G has a vertex which is not in a cycle of length four, then G is prime.
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