Prove that if A is an invertible n x n matrix, then adj A is an invertible matrix and -1 (adj A)-¹ 1 -A. det A

Q: 17. Let S denote the part of the cylindrical surface x² + y² = 9 that is between the planes z = -1…

A: A parametrization of the surface S is \)" data-mce-style="cursor: default;">S(u,v)=<3cos⁡u ,…

Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: For the signal below, sketch the following signals (c) æ(t+2) (d) x(-t) -t -2≤t≤0 0≤t≤4 otherwise…

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Q: Prove there is no real number a such that 28 + x6 + 1 = 2x³

A: The given equation .The aim is to prove the equation has no real solutions.

Q: Find the approximations Tn. Mn, and S, for n = 6 and 12. Then compute the corresponding errors ET,…

A: Thus, the integral value is 36.Let us assume..

Q: 1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10

A: To show that: P(n)=O(n4)We will use the definition of big oh notation to show this, we will find a…

Q: 4. (i) For an odd number n, suppose that 2" # 2 mod n. Can n be a prime? Explain. This is called the…

A: Eulers and fermats little theorem will used

Q: Find all the zeros. Write the answer in exact form. 4 q (x) = 2x² - 7x² + 3x² +8x-4 If there is more…

A: In this question we will find the zeros of the polynomial.

Q: Let A and B be 4 x 4 matrices such that and det (B) = 5. det (A) = -3 Find the following. • det (BT)…

A: If A and B be two square matrices of order n×n. k is a real number. AT is transpose of the matrix…

Q: Find the least-squares line given the matrix products ATA 608.4 5942.2 A¹b- = y = Ex: 1.2 +Ex: 1.2 €…

A: Let us to find a least square line for the set of values {(xi,yi):i=1,2,⋯,n}Let the equation of line…

Q: Find the f(t) for te-3t e-3t te-6t 1-te-3t F(w) = 6w (9+w²)²

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Q: 3. Solve the system of congruences Show the steps used. 3x = 2 7x 3 8x7 mod 7 mod 11 mod 19.

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Q: In a singular value decomposition of matrix A - V = 0.5 -0.71 0.41 -0.5 -0.5 0.5 U = 0.0 0.0 0.82…

A: The singular value decomposition of a matrix A of order m×n is defined as A=UΣVT , where U is a m×m…

Q: You wrote that a sequence is contractive if: |Xn+2 - Xn| <= |Xn - Xn-1|........ But I thought it…

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Q: Assume the domain of the field plot below is R2 a) Identify, if possible, a point in the plane where…

A: We have to answer the following questions on the basis of the given vector field.

Q: For any set A, both Ø and A are in the power set (A).

A: The power set P(A) of a set A is the set of all possible subsets of A, including the empty set (∅)…

Q: 6. LADW #2.2.1bf, page 46 (you only need to do (b) and (f)) - Note that you need to solve the system…

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Q: There is a circle whose radius r is changing with time t. We are interested in the area A of a…

A: (a) Area at We have given that now evaluated r and  at The initial area is

Q: The entire graph of the function h is shown in the figure below. Write the domain and range of h…

A: The domain is the collection of points where the function is defined. For this, we need to check the…

Q: All patients suspected of having a particular type of cancer are tested by two separate labs. The…

A: The probability that lab A produces a positive test for any patient with cancer P(A) = 0.27The…

Q: 3 2 7. ty'-2y=t³ sin(2t) − t³ +4tª; y(n)= · Use a graphing utility to draw a graph of the solution…

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Q: What is the likely amount of solutions to the problem xt = a in the field F*p and does is this…

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Q: Beulah and Biff invest in Bertha Fund. They make an initial deposit of $1,000. After 1 year they…

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Q: Use the given inverse of the coefficient matrix to solve the following system. 5x₁ + 2x₂ = 4 A. -…

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Q: (b) Prove that Z/4Z is not a field.

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Q: Let L₁ be the line passing through the points Q₁=(4, -2,-4) and Q₂=(3, 1, -7) and let L₂ be the line…

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Q: 1. Let Also let R = {(x, y, z) € R³ : 1 ≤ x² + y² ≤ 16, 0 ≤ z ≤ y +4}. = f(x - y) dv. R (a) Sketch…

A: (a)In cylindrical coordinates x=rcos⁡θ  ,  y=rsin⁡θ  ,  z=zThe region{(r,θ,z): 1≤r≤4, 0≤z≤4+rsin⁡θ,…

Q: Hello there, I don't understand the writing for problem 2. Can someone write the solution neatly?

A: We have to find here, D'Alembert's ratio test:If , then the series diverges and i.e., a limit does…

Q: dy Find eigenvalues & eigenvectors. = [²:2] Y dt 3-2

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Q: Let Z= (-1,2,2) be a point in R³. Find the closest point to Z that lies on the plane given by…

A: We have to find the closest point of  that lie on the plane

Q: lim s n where s₁ = 1, and S n+1 = (1 – = -)Sn n+31 for n ≥ 1.

A: We first evaluate the first few values of the sequence

Q: Compute the adjugate of A and use it to find the inverse, A-¹, 4 1 07 0 12 -3 0 1 A=

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Q: Let fn(x) = x^n for x ∈ [0,1]. check if it is pointwise convergence. Define where it becomes…

A: Given, fn(x) = xn , x ∈ [0,1].We will check poitwise convergence of fn on [0,1].

Q: Matrix A has 3 rows and 2 columns. Matrix B has 2 rows and 3 columns. Matrix C has 2 rows and 2…

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Q: An office tenant needs 3,550sf of usable space in which to operate their business. If they locate in…

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Q: Which of the following would form an equivalent relation? Given the set of people in the world, we…

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Q: Sketch the region enclosed by 2y = 3√x, y = 3, and 2y + 3x = 6. Decide whether to integrate with…

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Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace W-spand W = span{ a.…

A: We need to find two elements X and Y.

Q: Which of these statements never can be true? A) tanx = 500 B) Cosx =0,999 () sinxcosx 5,000 = Q)…

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Q: 2. Verify that n Re(Στ;) = ΣRe z; j=1 n Im)zj) =) Imzj. j=1 j=1

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Q: Exercise 6.1.10: Find the inverse Laplace transform of 251

A: We have to find the inverse Laplace transformation of the given function.

Q: you want. 1. Prove that the sequence an converges. The sequence is defined by ao = Task 2. Let an be…

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Q: Compute the work done by the vector field F(x, y) = (xy, x² + y²) when moving a particle…

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Q: x = 9 csc(t), y = 9 cot(t), 0 <t<= (a) Eliminate the parameter to find a Cartesian equation of the…

A: In this question we will find the Cartesian equation and graph.

Q: The total body surface area, or BSA, of a human is difficult to calculate. There are various models…

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Q: A club N with four members is shown below. N = {Aaron, Brad, Cindy, Dennis), abbreviated as N = {A,…

A: .

Q: The derivative of the function f is defined by f'(x) = x³ +3 cos (x² + 5). Find the x values in the…

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Q: Refer to the table below. Of the 36 possible outcomes, determine the number for which the sum (for…

A: Total outcomes are 36.Determine the number of outcomes for which the sum is prime.

Q: Use the bar graph from the World View "Comparative Output (GDP)" to answer two questions. 20.6 0.01…

A: Using a bar graph we have to calculate the percentage for given 2 conditions a. and b.

Q: The function f is defined by f(x) = x² - 2 - 4 sin (3x² + 5). Let l be the line tangent to the graph…

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