If M is the matrix: 1 3 5 021 7 -4 0 22-1 then what is IMI ? 4213 0 1

Q: 9x 4. y" -9y=3x 5. 4y" — y=xe*¹/2, y(0) = 1,y'(0) = 0 2y"+y'-y=x+1, y(0) = 1,y′(0) = 0 6.

A: y''-9y=9xe3x Finding the C.F D2-9=0⇒D=3,-3 Therefore C.F=c1e3x+c2e-3x P.I=u1xv1x+u2xv2x…

Q: Problem 1 Solve the following ODE using Laplace Table and partial fraction expansion 2+11+12y = 5 a.

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Q: b. 3x²y" + 6xy + y = 0

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Q: -0-0--0 and let V-Span(u, v). The linear transformation P:RR projects points orthogonally onto V,…

A: Given vectors P=-111-1 , u=-21-2-2 , v=-2102 Let V=Spanu,v is defined as V=-2-211-20-22. Linear…

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Q: (i) Given that I,,= x(lnx)" dx for n=Z, n≥0, show that (ii) I₁ = n e² 2 n 2 for all ne Zt. Find the…

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Q: Exercise 5: We consider the following matrices: 0 2 - - ( ) - ( ) - 0 - (9) B = 0 For the matrices…

A: A=020000AAT=020000000200        =400000000 The eigen value of the matrix AAT is 4,0,0 The eigen…

Q: Let k be a positive integer and let J be a k x k matrix defined as X 1 0 A 1 1 JK(X) 0 0 1 ⠀⠀ 1 0 0…

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Q: 1. y" + 3y + 2y = 2. 3. 4. 1 1 + ex y" + 3y + 2y = sin e* y" + y = sec Otan 9x y"-9y=3x 5. 4y" - y =…

A: Note :  '' As per our guidelines we will solve the first question . If you want any specific…

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Q: Let v = [1 3 -3] and consider the subspace of R³ spanned by the first two columns of 18 B 4 17 -3 =…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

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Q: Question 2: Use the Maclaurin polynomials in example 6.12 part (c) to solve the following. (You can…

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Q: 2. Consider the vector field F(x, y) = (M(x, y), N(x, y)) = (2x + 4y, 2x - 2y) graphed below. Find…

A: In the solution  we use  linear transformation for finding the matrix A .

Q: 5. 4y"-y=xe*/2, y(0) = 1,y'(0) = 0

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Q: Let S be the surface defined by the vector function R(u, v) = V2 / - 2u,v + 5, veu) for all (u, v) €…

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Q: Prove that 31 (n³ +5n+6) for every integer n ≥ 0.

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Q: Consider the following argument: If A, then B. It is not B. Therefore, it is not A. Which of the…

A: We have given an argument, If A then B. It is not B. Therefore, it is not A. Symbolically we can…

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Q: a) O Show that the wave equation Ytt = a²Yzz where a is a constant, can be reduced to the form Yuv =…

A: Use chain rule in a  and integration in b .c can be solved by substitution of t=0.

Q: 2. Show that Re(iz)=-Im z. 3. Show that Re(iz)=-Im z.

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Q: (a) Is z an increasing or decreasing function of x?? Of y?? (b) Is fa positive or negative?? How…

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Q: Prove the property of the Fibonacci numbers, F(n) = 5(n 4) + 3F(n-5), for n ≥6

A: We have to prove the property of the given Fibonacci numbers F(n) = 5F(n-4) + 3F(n-5) ,  for n≥6

Q: calculate the area

A: Given,            .

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

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Q: 1 2 20 3 3 0

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Q: +2³- 3. Prove that 1³+ n = n²(n + 1)² 4 for every positive integer n.

A: To prove : 13+23+33+43+…+n3=n2n+124 for every positive integer n.

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Q: Let F =Z2 and let f (x) = x3 + x + 1 ∈ F[x]. Suppose that a is azero of f (x) in some extension of…

A: Given: F=Z2 and fx=x3+x+1∈Fx and a is zero of f(x)  in some extension of F. To find : Elements of…

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Q: Determine if 21000 + 297 or 21000 + 277 or 21000 + 291 is prime.

A: Given numbers (a).  21000 +297,    (b). 21000 +277,    (c).  21000 +291. Determine if given numbers…

Q: 3. Consider the following propositions: p: 2 is the smallest prime. q:6 is a perfect square. Use…

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Q: The size of product BA is?

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Q: Consider the dynamical system Vk+1 = AVk where 01 Vo = - [6 and A- [86] = -8-6 Find a formula in…

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Q: a maximal element but no minimal element. Multiple Choice O о о The set of natural numbers under the…

A: Given : We have a four choices and we have to select one . To Choose: Which choice has maximal…

Q: a A LTI syst relating the response.

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Q: [p(-3) Define T: P3 → R¹ by T(p)=P(-1) where P₁ = {a+a₁t+₃²+⣣³ | 㵂 ª₁‚ ª. až are reals } C,…

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Q: d) Y(x, Solve the equations of part (c) for and, and show that t)=[f(x-at) + f(x + at)].

A: Ytt=a2YxxYx.0=fxYt(x,0)=0ϕx+ψx=fxϕ'x-ψ'x=0 Yx,t=ϕx+at+ψx-atYtx,t=aϕ'x+at-aψ'x-atYtx,0=0⇒ϕ'x-ψ'x=0…

Q: Find the coefficients of the Fourier cosine series for f(x).

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Q: Calculate fff sydv; where S is the regionin R3, in the first octant limited by: x² + z² = 4, y² + z²…

A: Given, ∫∫∫sydv where, S is the region R3 in first octant. Limited by x2+z2=4, y2+z2=4

Q: A) Find and draw the Fourie if(t) = cosat.cosbt

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Q: 3. Define primitive root and find all primitive root of following. (b) 19 (c) 15 25

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Q: Consider the dynamical system Vk+1 = AVK where 010 Vo and A 0 0 1 31-3 Find a formula in terms of k…

A: Given: A dynamical system define as Vk+1=AVk. Initial Value V0=706 and matrix A=01000131-3 To Find:…

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Q: 1. A fish hatchery employed a mathematician to design a model to predict the population size of fish…

A: Answer :-