1. Consider the differential equation 18y" - 9y' - 9y = -9y"" - 9u" - 18u' + 9u The input matrix of the state-space representation of this differential equation is: c. B = - d. B = a. B B = -1 ] 0 b. B = -A
Q: Prove that function f: Z x Z -> Z x Z defined by formula: f(m, n) = (4m + 3n, 3m +2n) is bijective.…
A:
Q: A series circuit has a capacitor of 0.128. 10° F and an indu 1.25 H. If the initial charge on the…
A: From LC circuit and Kirchhoff's Law we know d2idt2+1LCi=0 given capacitor C=0.128×10-6F and inductor…
Q: Dependencies in critical path analysis is/are The tasks that are required to complete a project. The…
A:
Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1² + 4e¹',…
A:
Q: Which adjacency matrix represents graph 67 O a Od POHOO PHO POHOO Ho 4 T 1 1 1 0 PTLOO 1 0 T 0 T 1 0…
A: We need to determine the adjacency matrix for the given graph.
Q: UTM Given two matrices AUTUTM -2 = UTI! UTM 1 2 3 1 0 1 By using Adjoint method, fi find and B - UTM…
A:
Q: Prove by contrapositive. Let k be an integer. If 5k+9 is odd then k is even.
A:
Q: Which set of edges below is the minimum spanning tree of graph G? 5 U 2 6 5 3 7 S 9 8
A: Given graph is Minimum spanning tree: Spanning tree of the graph whose sum of the weights of edges…
Q: For each table: 1. Identify the independent and dependent variables. 2. Identify units for the rate…
A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…
Q: Problem 4. Write the augmented matrix for the linear system that corresponds to the matrix equation…
A:
Q: A newly married couple bought a house for P175,000. They paid 20% down and amortized the rest at…
A: A newly married couple bought a house for P175,000. They paid 20% down payment and amortized the…
Q: Find a general solution to the differential equation. y" - y = - 10t+6 The general solution is y(t)…
A:
Q: 7. Let C be the portion of the circle x² + y² = 4 from (2,0) to (0, 2) traced counterclockwise. (a)…
A: We know if y=f(t) and x=g(t) then mass of the wire of an arc (f(t),g(t)) in a≤t≤b is given by…
Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0)…
A: Given DE is y"+2y'-8y=2e-3x-e-x ......(1) y(0)=1 , y'(0)=0
Q: Q1. Solve the differential equation using Frobenius method 2xy"+ (1+x)y' — 2xy = 0
A: 1. Given equation is 2xy''+1+xy'-2xy=0 To Solve: The differential equation using Forbenius method
Q: Sketch the vector field F(x, y) = (x − y, x - y) at the points (x, y) where x, y = {−1,0, 1}. .
A: We have to sketch the vector field F⇀x,y=-x-y, x-y at the points x,y where x,y∈-1,0,1. (x,y)…
Q: If f is continuous on [a,b], and f(x) ≥ 0 then > √ √F (2) dx=√√√°F (3) de f(x) dx a A B True False
A:
Q: The coefficient of xy13 in the expansion of (x + y)¹8 is O 43,758 O b 31,824 18,564 8,568 C Od
A: We know (r+1)-th term of binomial (x+y)n is Tr+1=Crnxn-ryr
Q: Pure water has a pH value of 7.0. How many times more acidic is milk, with a pH value of 6.4, than…
A:
Q: Lety be a circumference and let P be a point in the plane that lies inside y (but distinct from its…
A: Let us solve the given problem in the next step.
Q: A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a…
A:
Q: A surface has an equation of z² + 2x² + 3y² = 4. Through Stoke's Theorem, evaluate the surface…
A: Given- A surface has an equation of z2 + 2x2 + 3y2 = 4. To find- Through Stoke's Theorem, evaluate…
Q: Q2. Consider the function f: f(x, y) = x² − 4x + y² − 6y ] Find all critical points of f. Find the…
A:
Q: We learned a lot about power series in this chapter, and how they can represent most of the…
A: This is a problem of power series and fourier series.
Q: b) Use the power series method to solve the DE 6 (²+1)=0
A: (b). Given the differential equation y''-6(x2+1)y=0
Q: 2) Within the interval of convergence, a function formula and its corresponding power series are…
A:
Q: Solve each of the following congruences. (a) 6x + 3 = 4 mod 10 (b) 6x + 3 = 1 mod 10 (c) x² = 1 mod…
A: In congurent modulo n, ax≡bmod n has exactly 'd' solutions if 'd' divide 'b'where d=gcda,n otherwise…
Q: If G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G with H…
A: Given G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G…
Q: Use spherical coordinates to evaluate 0 0 0 2 2-r r-: (r² + z²) ² rdz dr d0.
A: As per the question we are given a triple integral in cylindrical coordinates and we have to…
Q: The nth partial sum of the series 2n=1 an is given by Select the correct rule for an or the actual…
A: nth partial sum of the series ∑n=1∞an is given by Sn=n+2n-3 hence an=Sn-Sn-1
Q: Shown below are matrix A and its rref, R. 3 A = -6 0 b. Find nullity (AT). 050 1 1 5 01 1 2] 00-4 5…
A:
Q: Let G be the solid bounded above by the plane y + 4z = 16, be- low by the ry-plane, and on the sides…
A: The given solid is bounded above by the plane y+4z=16, below by the xy-plane, and on sides by the…
Q: Find the general solution of the given differential equation using variation of parameters. П y" +…
A: We have to find the general solution of the given differential equation using variation of…
Q: Question: Given 4 training samples grouped into 2 classes (blue squares and red circles as shown in…
A: Given- Given 4 training samples grouped into 2 classes (blue squares and red circles as shown in…
Q: A single-input, single output system has the state variable representation a. b. O d. where A = =…
A:
Q: Problem 8. Define a transformation T: R2 R³ by T(₁, 2) = (-21 - 8x2, 6x1 + x2, 4x1 - 7x2). (a) Find…
A:
Q: Does the product of inversion in the circle of radius 1 centered at the origin with inversion in the…
A: Does the product of inversion in the circle of radius 1 centered at the origin with inversion in the…
Q: əz ди Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : (x²) dr du…
A: 3. Given Z=fx, y=4 ex lny and x=lnu cosv, y= u sinv To Find: ∂Z∂u and ∂Z∂v
Q: 29. In AABC, B = 49° a = 6 cm, and c = 14 cm. Solve AABC to one decimal place.
A: In triangle ABC, ∠B=49°a=6 cmc=14 cm We know that cosB=c2+a2-b22ca Substitute the values. So, cos…
Q: Given the graph of f'(x) below, where the Domf(x) = (-∞, ∞). Find the interval(s) for which f(x) is…
A:
Q: Your answer is correct. dy Write down a differential equation of the form dt all other solutions…
A:
Q: A nonhomogeneous equation and a particular solution are given. Find a general solution for the…
A:
Q: (b) 9₁ = -8y₁ - 2y2 y2 = y₁ - 4y2 e-6t + c₂te-6t and y2 = -c₁e6t+c₂(t+1) e-6t) (solution y₁ =
A:
Q: A pentagonal fractal pattern has the sequence (1, 5, 25, 125,...). The recursive formula is Ob OC a₁…
A: Introduction: One of the fundamental concepts in mathematics is sequence and series. A series is the…
Q: Given f(x) = (1+x)1/3, a. Determine the Maclaurin series up to n=3 expressed as a simplified…
A:
Q: Question: Show that S is a subspace of R2 where S = {x R² : x = (5k, 10k), k = R}.
A:
Q: A pentagonal fractal pattern has the sequence (1, 5, 25, 125,...). The explicit formu O a Ob Oc Od…
A: given sequence 1, 5, 25, 125, ... we know nth term of a geometric progression is an=arn-1 where a…
Q: A small company manufactures three different electronic components for computers. Component A…
A: Introduction: By entering predetermined values for the variables in the equations and finding…
Q: Please provide the answer, I don't know how you got to any of this if the answer is not clearly…
A: To find centroid of any solid region we need to find its mass and moment about co ordinate planes…
Q: Order 4 of the following sentences so that they prove the following statement by contradiction: The…
A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…
LINEAR SYSTEMS
Step by step
Solved in 2 steps with 2 images
- 100 3. Let A = 3 0 1 0 2 2 (a) (. (b) (. ) Find the cofactor matrix C -) Use the cofactor matrix to find A-1 =Express the system of differential equations in matrix notation. x' = 3x +9y y' = 4x-9y Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) tor OA. OB. OC.1. Write down the 3 × 2 matrix A with a;j = 2ij – cos 3
- Write down the 5 × 5 finite-difference matrix equation (h =) for du = f(x), du du (): dx (1) = 0. dx %3D dx?Find fhe inverge of the 2x2 matrix Cos & Sin t - Sint Cos o-1 b) Let P = (AB) ((AB)' (AB)) (AB)' (Assume the inverse exists). Solve the following expressions: i) P'. What does this tell you about the matrix P? ii) PP iii) P(B'A')' iv) x'(B'A')P'P(AB)x
- {H} Let B = and B' Find the change of base matrix from B' to B and from B to B'. (a-) Given the function , y = 4x2 + 9 i- Find the difference quotient as a function of x and delta x. ii- Eind the derivative dy/dx. iii- Find f/ (3) and f/ (4). (b-) solve the system by matrix Cramer’s rule. 4X1 + X2 – 5 X3 = 8 - 2X1 + 3X2 + X3 = 12 3X1 – X2 + 4X3 = 5Let P = (AB)((AB)'(AB))¯¹(AB)' (Assume the inverse exists). Solve the following expressions: i) P'. What does this tell you about the matrix P? ii) PP iii) P(B'A')' iv) x'(B'A')P'P(AB)x
- Matrix AA is transformed by a scalar to form matrix BB . A=[−1.5 3] B=[3 −6] [4.25 −2.5] [−8.5 5] What is the value of the scalar?Write the system of first-order linear differential equations represented by the matrix equation y′ = Ay. Then verify the general solution.Xn Let vn be the solution to the discrete dynamical system: Yn 6xn – 13yn Oxn – 7yn Xn+1 Yn+1 [:] -3 If vo find vn- -1 Put the eigenvalues in ascending order when you enter xn, Yn below. Xn = Yn = )"+ )" ||