Let A = a Show that det (A-\I₂) = λ²−tr (4)\+det(A), where tr (A) =a+d. c d (In general, the trace of a square matrix is the sum of the entries on the main diagonal.)

Q: Suppose that Vf(x, y, z) = 2xyze™² i + zeª²j+ yea² k. If f(0, 0, 0) = 4, find f(3,3,7). Hint: As a…

A: Given, ∇f (x,y,z) = 2xyzex^2i + zex^2j + yex^2k. If f(0,0,0) =4 , then we have to find f(3,3,7)…

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Q: coefficients.) 3 y"+10y' +29y=16t³-5t e sin 2t What is/are the root(s) of the auxiliary equation…

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Q: Suppose F(x, y) = (4x + 2y)i + (2x + 4y)j. Evaluate the line integral for each of the given paths,…

A: (a) ∮CF→·dr→=∮C4x+2yi^+2x+4yj^·i^dx+j^dy                =∮C4x+2ydx+2x+4ydy Let ,…

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Q: 1) Find the general solution, i.e. solution with precision up to some constant C, of the following…

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Q: use a property of the real numbers and explain how the property is being applied =14(3+(-x))+15x-51…

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Q: Let the n dimensional square matrices A and B be similar, i.e., PBP-¹. where P is a n dimensional…

A: The n dimensional square matrices A and B be similar. i.e., A=PBP-1, where P is a n dimensional…

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Q: A = -27 32 -18 8 -8 5 -24 23 -18 Recall that for x € C, e^x= Σæk/k! = 1+x+x²/2! + x³/3! + ... k=1…

A: Given matrix is: A=-2732-24-1823-188-85 Using ex=∑k=1∞xkk!=1+x+x22!+x33!+ . . .  we will define…

Q: -1 A-34] 1 Let A = 5 Find vectors X1, X2,. X; so that N (A) equals span {x₁, x2,...,xj}. ..y

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Q: 4) Finde'A, if A = -2 24 -2 32 1 -2 1

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Q: what does |B| mean

A: |B| denotes the cardinality of a set.

Q: II. Let G₂ be the solid above the xy-plane that is inside the sphere x² + y² + 2² = 16 but outside…

A: Given: Sphere: x2+y2+z2=16            Cylinder : x2+y2=12 Evaluate: I=∫∫∫G2 z dV

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Q: A = -1 1] 2 1 2 3 (a) Calculate each of the cofactors C₁, of the matrix A. (b) Use cofactor…

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Q: 21. Find an equation of the following function: (more than one possible answer) T T A sine function…

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Q: . F(x, y, z)= yz²i+xz²j+ (2xyz-5)k Determine if is a conservative vector field. If it ¡F-dr is, find…

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Q: Problem 2. Determine the solution to = 100 021 002 X, X(0) = (1,0,0)".

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Q: Let the sequence 9n be recursively defined by go = 0, 9₁ = 1, 9n = In-1 +29n-2 for n ≥ 2. Show that…

A: Given: g0=0, g1=1  and gn=gn-1+2gn-2  for n≥2. To show: limn→∞gn=∞.

Q: 3. We have the following function == -2r² - 4x - + 4y + 4xy (a) Find the stationary point (b)…

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Q: an Find the limit of the sequence whose terms are given by = = (n²) (1 - cos()).

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Q: 4. Given a propositional logic sentence: E: (P and (Q or R)) or (if (P and (Q or R)) then (P and Q))…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Complete the remainder of the table for the given function rule: y = -2x + 9 24 X-4 -2 1800 y 17 [?]…

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Q: Use the ordinary interest method to compute the time (in years) for the loan. Round your answer up…

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A: The given problem is to find the inverse Laplace transform of the given functions.

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Q: 6. The revenue function (in dollars) for a business is R(x)=-4x² +80x, and the cost function (in…

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Q: Eliminate the parameter and describe the shape of the curve: :=√√x+4; _y=3√t; for 0≤t≤16

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Q: Q4B. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {[a, b],…

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Q: Consider the regression equation In Y = 4.37 +0.2X₁ +0.3X2 a. Predict the value of Y when X₁ = 8.5…

A: Given Data: Let us consider the given regression equation: Yi^=4.37+0.2X1i+0.3X2i

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Q: solve the following give the general solution : question 1. y'=3y+15x+17 , y(0)=3

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Q: Interest has been described as a rental fee for money.  Explain why this is an appropriate…

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