Find the minimum and maximum values of the function subject to the given constraint f(x, y) = 12x² + 2y², 3x + 4y = 1 Enter DNE if such a value does not exist. f min = fmax =

Q: If B is the inverse of A 2, show that AB is the inverse of A.

A: A square matrix A is said to be invertible if there exists a square matrix B such that AB=I, where I…

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Q: 2. Determine the inverse Fourier transform of the following functions: a لمند 2// 1 ـ لما

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Q: For each divisor k . 1 of n, let Uk(n) = {x ∈ U(n) | x mod k = 1}. [For example, U3(21) = {1, 4, 10,…

A: For each divisor k > 1 of n , Uk(n) =x∈U(n)| xmod k =1. To prove Uk(n) is subgroup of U(n).

Q: equation of the the point (5-5/3) which plane 4y - 1+² 32 = 1 8+ X Find the The an

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Q: (1 point) Find the differential of the function w = dw dx+ = x³ sin(y526) dy+ dz

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Q: The subspaces of R3 are planes, lines, R3 itself, or Z containing only (0, 0, 0).(a) Describe the…

A: We know that ℝ3 is a vector space having elements of the form x, y, z, where x, y and z are the real…

Q: 1. Let A be an n x n matrix and x is a scaler. Show that det(x A)=x" det(A).

A: Solution:-          It is given that , A is any n×nmatrix and α is a scaler .…

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Q: Find a polynomial p(x) in Q[x] such that Q(V1 + V5) is ring- isomorphic to Q[x]/{p(x)).

A: We need to find a polynomial px in Qx such that Q1+5 is a ring isomorphic to Qx/px. We know that if…

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Q: A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm…

A: Consider the diagram as per give information,   It can be observed from the diagram the distance of…

Q: 16. Find the solution to each of these recurrence relations with the given initial conditions. Use…

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Q: 3. Use definition to compute the Laplace transform (a) L{t²} (b) Given Compute L{f(t)}. f(t) -{t =…

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Q: Describe differences between (fog)(x) and (gof)(x). Give examples

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Q: Use abbreviated truth tables to show that each of the following arguments is valid (fully explain…

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Q: determine all eigenvalues and corresponding eigenvectors of the given matrix.

A: Eigenvalue: A number λ is said to be an eigenvalue of a square matrix A if there exists a non-zero…

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Q: xy² R x² + 1 Round your answer to four decimal places. Find • dA, R= [0, 4] × [ - 2, 2]

A: We need to evaluate the integral: ∬Rxy2x2+1dA in the domain: R=0, 4×-2, 2. Use the provided limit to…

Q: Find x so that the dot product of the vectors u and v below is 23.

A: dot product will be 3*5+2*(-2)+2x so this must be  23

Q: (1 point) Use a graph below of f(x) = ln(8x² + 1) to estimate the x-values of any critical points…

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Q: Let a, b ∈ R with b ≠ 0. Show that R(a + bi) = C.

A: Given that a, b∈ℝ with b≠0. To prove that ℝa+ib=ℂ.

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Q: Sketch a graph of f(x) = ax +bx+c that satisfies the set of conditions below. a>0, b²-4ac=0 Choose…

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Q: a)A square matrix so that Ak = 0 is called a nilpotent matrix. What can you say about the…

A: I have given the answer in the next step. Hope you understand that

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Q: 4. For what values of o and w, if any, is the system [₁(t) [₂(t uniformly exponentially stable? = O…

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Q: Consider the solid under the graph of z = e above the disk x² + y² ≤ a², where a > 0. (a) Set up the…

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Q: Solve by Gauuss

A: We have given that a system of equations, 7IP+6I+8W=100006IP+3I+5W=75008IP+9I+4W=9000 We will use…

Q: What is the Fourier transform of the following function: f(x) = {sin4πx, x ∈ [-1, 1]; 0, for every…

A: Please find attachment

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Q: Which of the following is the general solution of the differential equation (e^x sin y + tan y)dx +…

A: This is an exact differential equation

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Q: How many Sylow 3-subgroups of S5 are there? Exhibit five.

A: To find the Sylow 3-subgroup of S5.

Q: sider the following series. (Enter your answers using interval notation.) Σ 7-1) n A-1 (a) For what…

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Q: Evaluate ſ√√x² + y² dA, where D is the domain in Figure 4 -RE D -R₂ IRE 20 R FIGURE 4 SSD √x² +…

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Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

A: Given objective function is p=x+2y Subject to the conditions x+y≥2x+y≤6x-y≤2x-y≥-2 The minimum and…

Q: 7.8 Prove, by writing it out in component form, that (a × b) × c = (ac)b — (b. c)a, and deduce the…

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Q: Write the general solution of the differential equation 2ydx + xdy - x^3dx = 0. In writing your…

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Q: Suppose that A to B and 69. B to C. a function from function from Show that if both & and I are onto…

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