Compute u×v. (a) u = 2i + 3j + 4k, v = −i + 3j − k (b) u = i + k, v = 2i + 3j − k (c) u = i − j + 2k, v = 3i − 4j + k

Q: 3) The impulse response of a certain linear system is h(t) = u(t) + d(t). Determine the zero state…

A: The zero state response for t≥0 is:  yt=ht*ute-t      =ut+δt*ute-t      =∫-∞∞uτ+δτut-τe-t-τdτ…

Q: Consider the simple linear model Y; = Bo + B1Xi + €¿, where e~N(0,0²); i = 1,2, .. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: x + 2y + z – t = 5 3 ,* + y+ 2z + 2t = 8 2 4x + 4y + 3z + 4t = 22 1 x + 5+t= 3

A:

Q: Given that the system zy² + zu + v 2r+ 2y-uv 2 zu + yu – ryz = 1 at (u, v) = (1,1)? can be solved…

A: Given system of equations as follows, xy2+zu+v2=3x3z+2y-uv=2xu+yv-xyz=1

Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

A:

Q: In a mechanical system, acceleration a , velocity v, and distance S, are related by the simultan…

A: Given equations are 4.8a - 12.6s + 6.5v = -13.9    → (1)5.2a + 4.7s - 3.6v = 6.8          →(2)-3.3a…

Q: Let A(t) be a n × n matrix whose coefficients are continuous functions of t on the interval (α, β).…

A:

Q: (b) Use Cramer's rule to solve for y without solving for the unknowns x, z, and w. 4x+ y+ z+ w= 6…

A: Crammers rule is applicable to a system that have non zero determinant for the coefficient matrix.…

Q: 1. Find y by Cramer's rule for the following linear system. I+Oy+22 6 -3r+4y +62 30 -r-2y+3z=S

A: “Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find solutions of the linear PDE u, + yu, =0 , given that u(0, y)= y'. ди(х, у) ди(х, у) Notation is…

A:

Q: If z = f (u) + g(v), where u = = and v = x ·y. Prove that Q1: x· Zx – y· Zy = y² · Zyy – x² · Zxx…

A: We have z=fu+gv, and u=xy  and v=x.y We need to use the chain rule and prove x.zx-y.zy=y2.zyy-x2.zxx…

Q: Given that the system xy² + zu + v² = 3 x³z + 2y – uv = 2 xu + yv – xyz =1 can be solved for x, y,…

A: Given that,

Q: Compute u x v. (a) u = 2i + 3j+ 4k, v = -i+ 3j – k (b) u =i+ k, v = 2i + 3j – k (c) u =i-j+ 2k, v =…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Consider the following nonhomogeneous linear system: xi = 3x1 + 4x2 + 10 cos t x2 = 3x1 + 2x2 3.…

A:

Q: Show that the homogeneous system (a − r)x + dy = 0 cx + (b − r)y = 0 has a nontrivial solution if…

A: a-rx+dy=0cx+b-ry=0 The coefficient matrix is, A=a-rdcb-r Now if the system has nontrivial solution,…

Q: The system in Section 3.2 - Exercise 3 (previous page): dy dr 5x + 4y dt 9x dt

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: 23. Solve the Cauchy problem 1 (r+ y) uz + (r – y) uy = 1, u (1, y) = %3D

A: Given: x+yux+x-yuy=1 , u1,y=12

Q: There are two functions: fj =0.6+6x1 Cos x2 =0 and f2 =8x; +7Sinx2 +10=0, then for the initial…

A:

Q: The matrix has a singular value decomposition A = UEVT where and and The 2,1 entry of U is (U)21 =…

A:

Q: (b) Find the Wronskian W[y1,Y2](t) of y1 and y2-

A: W[y1,y2]= -t2et

Q: If z = f(u) + g(u), where u = = and v = x · y. Prove that x · Zx – y · Zy = y² ·Zyy – x².Zxx using…

A:

Q: In Exercises 19–22, verify that (u X v) •w = (v × w)•u = (w X u)•v and find the volume of the…

A:

Q: Let f(z) = kz5 + az3 + cz.  Find u(x,y) if z = 3.8 + 6.8i , a = 6, c = 9, and k = 3. Round off your…

A:

Q: Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) x to find a solution…

A:

Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

A:

Q: Find the value of x, y, & z using Gauss Jordan Method x+ 2y + 6z = 15 3x + 4y + z = 16 6x - y - z =…

A:

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 5 x + y + z + W = -7 5x + 3y - z +…

A: Here we have to use cramer rule for solving the system of linear equations

Q: 9. Solve u +u =0 for 0≤x≤1, 0≤ y ≤1, given u(x,0)=0, u, (x,1)=0, u(0, y) = 0, XX yy u(1, y) = 1.

A:

Q: Determine which of the following is the Jacobian matrix for the system given by dx 3 = 3x?y³ -xy? –…

A: Jacobian Matrix: Given that,

Q: Find the solution of BVP ۱۰uny U₂+2; u(0,4)=0 2 ux (2,0) = X₂

A: As per the question we are given the following boundary value problem (BVP) : uxy = ux + 2  ;…

Q: a. Is S = {v1, V2, V3} linearly independent

A:

Q: Use the operator method described in this section to find the general solution of each of the…

A:

Q: Find (x ,y, z) by using Jacobi or Gauss of Gauss Jordan method 5z — Зу + х%3 -1 2y – z = 2 z - 4x =…

A:

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: 5. Compute the solution to the original system of equations by transforming y into x, i.e., compute…

A:

Q: Let T(z) = -6z* +z² –1 and U(x) = 2z – 4x + 3. Find T(z) +U(z) %3D OA. -6z4 + 2z3 +z² - 4z + 2 OB.…

A: Let Tx=-6x4+x2-1  and Ux =2x3-4x+3

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=

A: Given that, u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v

Q: Solve for r and y the following system of simultaneous equations 2 In(z) = In(y) + In(16) %3D e e =…

A: Solution: As per given data e have two simple equation, 2ln(x)=ln(y)+ln(16) exey=e4 where,'x' and…

Q: Use the method of undetermined coefficients to determine only the form of a particular solution for…

A:

Q: Consider the system defined by: O a. O b. 0 с. O d. X = AX + BU 0 1 B = 0u(t) [3] -2 -3] The…

A: Which is the characteristic equation.

Q: Find the equilibrium state of the dynamical system Xn+1 = 0.4xn+0.4yn, Yn+1 = 0.6xn +0.6yn- By…

A:

Q: 10.Use Cramer's rule to solve the linear system. 3x+ 5y = 8 y+z = 3

A: NOTE: Refresh your page if you can't see any equations. . system Ax=b is  the matrix A is

Q: Find the Wronskian of a given set {y1, Y2} of solutions of (1 – a²)y/" – 2ry' + a(a+ 1)y = 0 when…

A: According to the given information it is required to find the Wronskian of solution set

Q: 1. Find y by Cramer's rule for the following linear system. x+Oy+2z 6 - 3r+4y+6z= 30 -r-2y+3z S

A:

Q: Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given…

A: To find the solution for the below linear differential equation system. x'=−14−90214x,  x0=02

Q: Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) 1x to find a solution…

A:

Q: 1. Find y by Cramer's rule for the following linear system. x+Oy+2z=6 - 3r+4y+6z=30 -r-2y+3z=8

A:

Q: Solve and find the response of a linear second-order system described by (dy^(2))/(dt^(2))+3…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.