# Examples for college students

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 67

- Derivation

Exists a function whose derivation is the same function? - The determinant

The determinant of the unit matrix equals 7. Check how many rows the A matrix contains. - The inverse

The inverse matrix for matrix A has a determinant value of 0.333. What value has a determinant of matrix A? - Inverse matrix

Find how many times the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix. - Determinant 4137

The determinant of matrix A has the value 2. What will be the value of the inverse matrix determinant to matrix A? - Determinant 4161

The determinant of the inverse matrix to matrix B has a value of 0.25. What is the value of the determinant of matrix B? - Distribution function

X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5 < ξ < 3.25) p(2.8 < ξ) and p(3.25 > ξ) - Second-order 5138

What is the rank of a second-order square matrix if we can say that this matrix is regular? - Second-order 5170

What is the rank of a second-order square matrix if we can only say that it is singular? - Geometric 5895

A2 + a3 = -6 a1 + a2 + a3 + a4 = 20 Geometric sequence q, a1? - Complex plane mapping

Show that the mapping w = z +c/z, where z = x+iy, w = u+iv and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane. - Unknown number

I think number. If I subtract from the twelfth square the ninth square, I get a number 27 times greater than the intended number. What is this unknown number? - Equations 18023

Solve a system of equations with four unknowns: 2a + 2b-c + d = 4 4a + 3b-c + 2d = 6 8a + 5b-3c + 4d = 12 3a + 3b-2c + 2d = 6 - Matrix 5221

The rank of matrix A is 3. What rank will this matrix have if we add twice the second row to its first row? - Function 59513

Expand the function f (z) into the Laurent series at point z0 for the given annulus f (z) = 1 / ((z-2) * (z-3)) a) z0 = 2, 0 3 - Applicants 42261

Of the 4,500 applicants, 2/9 were successful in the university entrance exams. How many applicants were successful? - Elimination: 10441

Solve the linear system of equations by Gaussian elimination: 3x1 −2x2 −5x3 + x4 = 3 2x1 −3x2 + x3 + 5x4 = −3 x1 + 2x2 −4x4 = −3 x1 - x2 −4x3 + 9x4 = 22 - Diameter 4111

How many balls with a diameter of 3.25 cm with a mixture in a circle with a diameter of 27 cm? - Balls

We have n identical balls (numbered 1-n) selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides wi - Probability 9771

What is the probability that ten molecules will arrange within the brown motion to be one molecule in the lower half and nine molecules in the upper half in one vessel?

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