Consider the DFA M = ({q0, q1, q2, 93}, {0, 1}, 8, go, {41, q2}), where d is defined as follows. 8(40, 0) 8(q1,0) = q1. 8(q1,1) = q1 8(q2,0) = 43, 8(42, 1) = 42 8(43, 0) = q2, 8(q3, 1) = q3 = q1, 8(qo,1) = q2 %3D

Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

A:

Q: What is the 4-point DFT of x = (0, 1, 0, 1) ? O(1, 1, 1, 1) O (2, - i- 1, 0, i-1) O (2, 0, - 2, 0)…

A:

Q: Use Cramer's rule to fins a solution: 3x-2y=4 6x-4y=0

A: Cramer’s rule:

Q: Evaluate | Vtan a sec" zdx. O a. 2 z tani z +tani +C 2 O b. 2 tani æ + tan +C 2 Ос. 2 O c. 2 2 t…

A: To evaluate the integral,  ∫tanxsec4xdx Rewrite the term sec4x=sec2x·sec2x…

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: X + x, + 4x, 9х, = 7 X2 2х, + 6х, 17x, = 5 2x2 4x, + 9x, 25х, 12x, = 4 = 7 4x4 explain the solution…

A:

Q: Find an upper triangular U (not diagonal) with U2 = I which gives U = u- 1.

A: Given, U2=I

Q: Exercise (7): Find f, zdxdydz on [0,1] × [0,2] × [0,3]

A: we have to find the following integral

Q: Verify that det A = det B + det C, where Uj + vj U2 + v2 Uz + V3 A = A22 аз1 A32 --EE-E: A12 A22 V2…

A:

Q: 3 Rnd the lineasion of the hunctran f(xLcos line asiz l

A:

Q: Why the 1st row and 1st column of the JACOBIAN MATRX is always Zero ?

A: It is not necessary that the 1st row and the 1st column is  always zero. It may be possible or it…

Q: Consider model y = B1+ B2 x2 + B3x3 + B4x4 + B5x5 + e Proof that SST=SSR+SSE for this model

A: SST is the sum of squared difference between the observed variable and its mean. It is called sum of…

Q: Find the meteix A of the Lineak teansfoRmati on foom IRto IR . 2. given by x2

A:

Q: 5. What is UF, where F = Ø? Prove the correctness of your %3D | computation. answer

A:

Q: Use the result of Exercise 41 to show thatf1−α,ν1,ν2 = 1fα,ν2,ν1

A:

Q: Which elements are invertible in Z4[x,y]?

A: W need to find elements which are invertible inZ4x,y.

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: Save the following Sef of Lincay equations using over relaxoation 10X, +X2 + X3 12 X, + 10X2 + X3 =…

A: Rewrite the given system of equations, to find x1, x2 and x3. Multiply each right hand side…

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: The article cited in Exercise 20 also gave the followingvalues of the variables y 5 number of…

A:

Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0<x<1 E(x)= nθvar(x)=nθ(1-θ)…

Q: 4: verify that wy = Wyx . ریاضيات المرحلة الثانية a w = In (2r + 3y) %3D

A:

Q: 2x+ 3y-z =1 4x + y-3z = 11 3x- 2y +5z =21

A:

Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

A:

Q: Exercise (7): Find f, zdxdydz on [0,1] x [0,2] x [0,3]

A: Find: ∫∫∫Vzdxdydz on 0,1×0,2×0,3

Q: Use linearization to approximate In(1.2).

A: we can use the following formula for approximate calculations: f(x)≈L(x)=f(a)+f′(a)(x−a). where the…

Q: Soluti 03 16. A 11 22 1 Let Ax- b be a linear svstem of n eauations in n unknowns, and assume that A

A: Given: A = 03-2114225, b = 75-2  and Ax = b To find: The value of matrix x.

Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: Find a mat rix P such that 30 P%= 1 2 30 0 2 1 0 OAP = %3D 3 -1] 1 0 OB P -3 1 -1 0 OcP = %3D 1 0…

A:

Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

A:

Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

A:

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: Evaluate ff xydxdy over the square with corners (0,0), (1,1), (2,0) and (1, –−1) (u + v) (u - v) 2 2…

A:

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-

A:

Q: 3. 2. If A is 2x2 matri x aud Á = A, but %3D A+ A. show that A= 0

A: The solution is :

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: In Exercises 47-50, verify that wy Wyx- 48. w e+ x In y + y Inx

A: To find the second partial derivative of any function z i.e., zxy first differentiate z partially…

Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Consider the first order linear PDE и, (х, у) + 2и,(х, у) + u(х, у) %3 4х. Find its general solution

A:

Q: 2. is it or divery Con

A: To solve the problem and find its convergence

Q: Prove that du Inlul + C where n= -1 u

A:

Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

A:

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

A:

Q: Find the orthogonal projection of v on the solution space of the linear system Ax = 0, where v = (5,…

A: The solution is given as

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: s convex.

A:

Q: Find leng th of the Cardioid Vsa6 from e -oto0 - 1 %3D

A: Use the formula of the length of the polar curve. L=∫0πr2+drdθ2dθ Here, r=aθ3 and drdθ=ddθ(aθ3)=3aθ2…