Independent work 1-4 Mathematics RFEI

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Independent work №1 of educational discipline "Mathematics" contains the following tasks:

I. Search for any value of the parameter α determinant | A | = 0 (a first assignment means a six similar from 1.1 to 1.6)
II. Find the value of the determinant | A | (And six similar assignments from 2.1 to 2.6)
III. Find the track set below the matrix (two jobs)
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VIII. Find the rank of: (two assignments)
IX. At what value of the parameter λ the matrix A is not backwards? (two assignments)
X. Solve the system of linear equations (4 tasks from 10.1 to 10.4)

1. Determine the beginning of the vector a = {2, -3, -1} if its end coincides with the point (1, -1, 2).
2. Find the length of the vector a = 2i + 3j-6k.
3. Find the angle between the vectors a and b, if a = (1, 2, 3), b = (6, 4, -2).
...
17. Find the coordinates of the foci of the hyperbola (X ^ 2/16) - (Y ^ 2/9) = 1.
18. Find the coordinates of the foci of the ellipse (X ^ 2/16) + (Y ^ 2/9) = 1.
19. Find the eccentricity of the ellipse (X ^ 2/16) + (Y ^ 2/9) = 1.
20. Find the sum of the lengths of the major and minor axis of the ellipse (X ^ 2/100) + (Y ^ 2/36) = 1.

1. Find the limit lim (X → 4) (X ^ 2-16) / (X-4);
2. Find the limit lim (X → ∞) (X ^ 3-4X ^ 2 +6) / (X ^ 4-2x ^ 3);
3. Find the limit lim (X → 0) (sin3x) / (X);
...
18. Calculate the area of the figure bounded by the graphs of the function y = 0, y = x, x = 3.
19. The body is in motion, described by S (t) = 6t ^ 2-12t. What will be the speed of the body at time t0 = 2c?
20. The formula for calculating the volume of a body of revolution about the axis Ox is:

Problem 1. On a shelf shopping mall lined with 6 packs of markers of different colors. What color combinations are possible to make, if the package of markers spread in a line?
Task 2. How many permutations of the letters of the word "business" in which the letter "b" in the first place, and the letter "c" - at the end of words?
Problem 3. What three-letter "words" can be formed from the letters of the word "accounting"? A word is any sequence of letters.
4. Task 4. How many ways can sit 6 participants at the round table?
...
Problem 13. Two furniture factory supply warehouse shopping center office furniture. Then the furniture in random order exhibited in the shopping center of the room. The probability that the first furniture factory standard, equal to 0.7, and the second - 0.9. Find the probability that at random taken office furniture - standard.
Problem 14. A discrete random variable has a probability distribution law: Xi = | 1 | 3 | 5 | Pi = | 0,5 | 0,1 | 0,4 |
Find the expectation M (X) is a discrete random variable X.
Problem 15. Find the expected number of defective cars 1000 cars are on the Kursk station, if each car may be defective with probability 0.03.