Let Consider the dynamical system x' (t) = Ba(t), where B is a 2 x 2 real matrix that is simila to 202212A (I2 denotes the 2 x 2 identity matrix). Then the origin is an attractor. a repeller a saddle point a spiral point [2022 -1 A = 1 2022 a center

Q: Let V and V" be vector spaces over a field F and let f: V→V' be a linear map. Which of the following…

A: Given that v and v' be vector spaces over F. Let f:v→v' be linear map. Kernel of linear…

Q: The binary operation ab=a+b-3ab is defined on Q. Select the correct statements. Select the correct…

A:

Q: Express f(x)= 1 = tan 4 (Hint: Use Integration as a power series and find its radius of convergence.…

A: We have to find the power series representation of f(x)=14tan-1x4. We know  11+x=∑n=0∞-xn replace x…

Q: Solve the system using Laplace transforms or by the operator method dy dx =-Y = -4x + 3 7 x (0)=√y…

A: We have to solve the system using Laplace  dxdt=-ydydt=-4x+3x(0)=74, y(0)=4

Q: x(t) = 1 + 2cos(t) y(t) = 2sin(t) t = [0, 2π] x(t) = -2- 7t y(t) = 6 + 4t te R x(t) = -2 + 5t y(t) =…

A:

Q: Solve using variation of parameters: y" - 2y + y = e/(1+t2) + 3et Yp= u₁ et + u2 tet (Use 2 decimal…

A:

Q: 3. Let f(x, y, z) = 9 (√√x² − 4y² + 2²) √√x² + 16y² + 2², where g is some nonnegative function of…

A: Given: Let us consider the given data, fx,y,z=gx2-4y2+z2×x2+16y2+z2 The surface S is given as,…

Q: A scientist satisfies the equation: (a) (b) (c) Q(t) of a substance present at ti 40"(t) + 4Q'(t) +…

A: The amount of a substance present at time t≥0 satisfies 4Q''(t)+4Q'(t)+Q(t)=0

Q: 1 -= 1+ n Show that the harmonic series Σ=1 Express 7. 12345 as a ratio of integers. 1 2 + 13 1 +…

A:

Q: Q.8 (a) Find the eigenvalues and eigenfunctions of the integral equation g(x)=2(2xt-4x²)g(1) dt

A:

Q: Lercise 8.13. (a) Is S₁ ≈ Z4 U(7)? Justify your answer. Is S4 Z6 U(5)? Justify your answer.

A:

Q: 6. y' = x + y², y(0) = 0; y(0.5) 8. y' = xy + Vy, y(0) = 1; y(0.5)

A:

Q: Exercise 8.8. Let p be a prime. Prove that ZpZp has exactly p+1 subgroups of order p.

A:

Q: round

A:

Q: Axes of Ellipse The following equation defined an ellipse. 212-21 2+2x₂²: = 1 Find the vectors of…

A:

Q: Use the method of your choice to find the volume of the solid generated by revolving the region…

A:

Q: 10. Let A be an n x n matrix such that for every x ER", ||Ax|| = |x|| (the norm here is the one…

A:

Q: a) z=4x²-9x²y+2y³, com x=2 sen(t) e y=cos (t); b) w=xe, com x=4t², y=5e²¹ e z=2t². c) z=x y²+2x²,…

A: Introduction: When the independent variables of a function is again dependent on a single parameter,…

Q: II. Use the Remainder Theorem to find the remainder when each polynomial is divided by the…

A:

Q: 8. Let T: M₂2 → R² be defined as 7 ([a b]) = (a − b, cd). Determine whether or not 7 is a linear…

A:

Q: 4. Let S be the triangular region in R3 with vertices at (2,0,0), (0,6,0), and (0, 0, 3) with upward…

A: Given Data:  It is given that S be a rectangular region with vertices (2,0,0), (0,6,0) and (0,0,3).…

Q: Consider the following initial value problem: y" + 10y' + 21y = d(t − 5) + u₁0(t); _y(0) = 0, y'(0)…

A: Since you have asked two questions, here is the solution of part (a).

Q: Consider the following points. (2, 4), (3, 6), (5, 10) (a) Determine the polynomial function of…

A:

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 20 -6 -6 -3…

A: To Find: The inverse of the matrix(if it exists).  20-6-6-311-312

Q: Number of voters 1st choice 2nd choice 3rd choice 4th choice 5th choice 506 Points for candidate A:…

A: In this question, the concept of Baroda Count is applied. Baroda Count Points are assigned to…

Q: Q 9) Does the series: ∞ ∑    1/4n-1 n=1   converge or​ diverge? Give a reason for your answer.…

A: Use series integral test.

Q: Exercise 8.3. (a) If H₁ and H₂ are subgroups of groups G₁ and G₂, respectively, prove that H₁ÐH₂ ≤…

A:

Q: Solve the given differential equation. All solutions should be found. x³-8y x dy dx NOTE: Use c for…

A: To Solve: The given differential equation. dydx=x3-8yx

Q: IR2 be defined as T ([a b]) = (a - b, cd). Determine whether or not I' is a linear 8. Let T: M22 ->>…

A:

Q: Consider the diagram below in a two dimensional Cartesian x-y plane. The parabola is given by the…

A: we will use symmetry of given figure about y-axis and condition of quadratic equation to find…

Q: The function f is defined as follows: f: R² R² with f(x, y) = (2x, x+y) Which statement is correct?…

A:

Q: ²=0.2P(1-5). 4. A certain population can be modeed by the differential equation - dP dt where P(t)…

A:

Q: Mr. Smith has a classroom with a row of 8 desks. Suppose that Jessy and Jenna are part Mr. Smith's…

A: Case 1 jessy and Jenna can be seated in 1 and 5 position case 2 jessy and Jenna can be seated in 2…

Q: Consider the Initial Value Problem: (a) Find the eigenvalues and eigenvectors for the coefficient…

A:

Q: Set up an integral for the circulation of F along the curve C, where F = (x² + y², x² - y²) and C is…

A:

Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: Which equation represents the graph below? WEST

A: We have to determine the equation of the given graph. For this, we have to find the roots of the…

Q: Find all the sylow 2 subgroup of D5 and show explicitly that they are conjugate

A: Given That : sylow2-subgroup of D5 To find : sylow2-subgroup of D5 and also show that they are…

Q: Let V=R² and S = {(0,y) y R). If=(1,0), then what is the cosetu + S. O The line y = x. O The line y…

A:

Q: (b) A linear system has the form dy dt y(0) = (1,0,0) Suppose the eigenvalues of A are 2₁ = -1,2₂ =…

A:

Q: A small company has 5 part time employees and 10 full time employees. Of the part time employees, 3…

A: Introduction: In random experiment, mutually exclusive events are very important. These events are…

Q: Find a differential equation that corresponds to the given direction field. Consider differential…

A: We need to determine the differential equation of the form: y'=ay+b corresponding to the given…

Q: Ive the following PDE with nonhomogeneous boundaries: PDE UttUxx = 0, BCs u(0, t) = sin(t), u(L, t)…

A:

Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then £¹{F(s)G(s)} = f(t)g(t). O True O…

A:

Q: Write an expression for the apparent nth term an of the sequence. (Assume that n begins with 1.)…

A:

Q: Prove the following statement: for all integers n> 1 1³ +2³+ 2 = [ n(n+1)]² 2 + n³ = [ 3

A: To Prove: The following statement: for all integers n≥1 13+23+...+n3=nn+122

Q: Given: n(A) = 14, n(B) = 22, n(A n B) = 6 Find n(A U B) O 36 O 42 022 O 20 O None of these

A:

Q: dy Write down a differential equation of the form = ay + b whose dt all other solutions diverge from…

A: Hint: Assume the first order differential equation in the given form so that when t→∞ then solution…

Q: The figure to the right shows the letter L in a rectangular coordinate system. The figure can be…

A:

Q: Which of the following does not exist? a. multiplicative inverse of 7mod16 b. multiplicative inverse…

A: