4. If A is a nonsingular nxn matrix, show that AA¹ is nonsingular and det(AA) > 0.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. P 3.f(t)= te2t sint IMAL

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Q: 3. Let What is (CA) U B? (a) {x € Z] x % 4 = 2} \ {10} (b) {x€N | x % 4 = 2} \ {10} (c) {x€N |…

A: Using the way in which the sets are defined we solve the problem. The typeset solution in latex is…

Q: 2 -3 -5 5 2 -2 Let A = အားကြည့်ကြပါ 5 B - 1 -3 -5C - 3 4 Find: -3 -4 -1 3 5 -3

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A: Given: X'1=7X1-5X2,      X'2=4X1+3X2 The above two equation written into matrix form X'(t)=7-543X

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Q: . The collection {On}, where On = (1/n, 1-1/n), is an open cover of the set A = [1/2, 1). Find (a)…

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Q: 3. 2x₁ - x₂ 2 X x, - 3x2 + X3 = -2 -X, + X2 - 3x3 = -6 ||

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Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. Jell 2. f(t) = cosh wt sin wt

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Q: If matrix of transformation A is both invertible and orthogonally diagonalizable, then A-1 is…

A: Answer is True

Q: Let f be a real-valued function continuous at the point a = (a1, a2) in R². Keep a2 fixe and define…

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Q: Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 5i and corresponding eigenvector -1+ =…

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Q: COMPLEX ANALYSIS Please answer all questions Show that e.e=e+w for any z, w € C.

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Q: Identify and sketch by hand the graph of the quadric surface 36x² − 9y² +162² +36y - 180 = 0. You…

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Q: For 1 ≤ y ≤2: R = 1 For 0≤ y ≤ 1: R = 1 r=0 Plane region € Ay Ay

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Q: L {sin(wt + O)}; w and O are constants

A: The solution is given as

Q: 3. 4. 6 5 8 4 9 58 4 3 2 5 9 4 7 26 5 93 7 8 8 9 2 9 2 7 4 9 8 2 5 5 2 6 3 6 3 7 9 7 1 5 8 7 3 9 8 4…

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Q: Use variation of parameters to find a particular solution, given the solutions y 1, 2 of the…

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Q: a) f: Q- Q defined by f(x) = |x| for all x € Q. b) g: C-M₂ (R) defined by g (a + bi) = a b -b a h:…

A: This is a problem of ring theory.

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Q: Let f (0, 1] → R such that f(t) = t-1/2. Prove that f is Lebesgue integrable over (0,1]. (Hint:…

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Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. 1.…

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Q: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: Let f be a real-valued function continuous at the point a = (a1, a2) in R². Keep a2 fixed and define…

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Q: What is the answer if A= 4    5   0  and B= 1   0    0   are multiplied by each other?…

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Q: Find the nth term of the following series: 1.) 3 + + + 21+ 2 .... 2.) 1 − 4 + I 1055 10! +

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Q: 1. Iff: [0, 1] R is defined as f(x) = x if x is rational, 1-x if x is irrational, discuss the…

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Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

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Q: Use Green's Theorem to evaluate the line integral Scox (y - x) dx + (2x - y) dy for the given path.…

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Q: Let be a function that allows continuous second partial derivatives, we know that: Vf(x, y) = (16x³…

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