a) Prove that Hermitian, skew-Hermitian, and unitary matrices are normal.

Q: Determine the following: (a) Cycle decomposition of o. (b) 2-cycle decomposition of o. (c) Is o odd ...

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Q: 2. Let f(r) = r² and let e > 0 be given. (a) Find ő so that z – 1| 2 and you had to find a ô so tha...

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Q: Find the order of each element in Z12-

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Q: 5. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains ...

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Q: -4 Evaluate [g(x)]g'(x)dx.

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). In this probl...

Q: 3. (а) Determine all distinct values of v2A given that A = -1+ iv3. (b) Given f(z) = z² – 3ixy. (1) ...

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Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^. ...

Q: he General so SO 1 xD +D

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Q: The type of the partial differential equation ô’u ô'u -4- 6- = 2x+y is 2

A: The type of second-order partial differential equation (PDE) depends on the sign of its  discriminan...

Q: Example 4: Draw the image for a dilation with a scale factor of -. A scale factor of - means the ima...

A: Any point on the cartesian coordinate system is defined as x, y.  Start from the origin, move p unit...

Q: The price of a car depreciates by 15% each year. Find the price of a car after two years that is cur...

A: Given: The price of car deptreciates by 15 % each year. Hence, it can be determined that the price o...

Q: (e) f(x1,x2) = xỉ/x2 on R x R++.

A: The solution of (e) is in below

Q: Create one word problem involving Business Math’s Profit and Loss. With solution

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Q: 6. :- 2xy)y' yly+ sinx] ;when x 0, y = 1

A: 6 Given differential equation is 11+y2+cosx−2xyy'=yy+sinx......1 and x=0, y=1. Simplify equation 1 ⇒...

Q: -2 ,入2 = 0 3 Let P be a 3x3 matrix having characteristic roots 21 and 23 = 1. Define Q = 3P3 – P2 – ...

A: Given that the characteristic roots of matrix P are λ1=-23, λ2=0, λ3=1 and Q=3P3-P2-P+I3, R=3P3-2P

Q: Find the error propagated from the function y = 3x* if an error of 0.06 occurs in the independent va...

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Q: y2 -y' | x(х + у) a. - xy = c+2) (G+2) ху? + 2ry' + = c ху — С 3 a. b. xy? = c (,+2 2x3 + 6ху? + 3ху...

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Q: The nature of the stationary point (0, -1) for the function f(x,y), if f= 4-12x, fy= 0 and fry=-4+ 1...

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Q: Show all work with hand calculation. Using the formula uploaded in the image below, find the h1 and...

A: There is no such introduction for the solution.I have explained it within the solution.Please go thr...

Q: a,b are two vectors then ax {ax (a xb)} =? ans. lal (6 xa) lal (a xb)

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Q: (2) Let (x, y) E R X R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and s(x, ...

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Q: naximum value of f(x)

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Q: i Let f(x) = r° and c= 0.01. Find an interval (a, b) containing c such that f(x) > 0 for all z € (a,...

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Q: 3.5.7 . (2n+1) If an thenlim a =? 2.5.8. (3n-1) ans. 2. 8. 1.

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Q: 4. A conical tank holds about 549.5 cubic feet of water. The tank is 21 feet tall. What is the radiu...

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: 1 a a? 1 For a real number a, if the system 1 of a a y a? 1 linear equations, has infinitely many so...

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Q: dz +eltz + e*² = 0 dt

A: We have to find the general solution of the differential equation dzdt+et+z=0, where z is the depend...

Q: Let L = {6, 12, 18, 24, . . .} be the set of multiples c let M = {45, 90, 135, . . .} be the set of ...

A: Introduction: The objects in a set are referred to as their elements (or members); the elements are ...

Q: 글 (n3 + 1) 2 [Hint: Σ=1x3 = (1)3 + (2)3 = 9]

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Q: 10. A jogger runs 200 m in a direction 30° east of north and then 100 m in a direction 35° south of ...

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Q: 4Express tha answer in scientific notation a) (31 xl)»(650) b) o. 000 o78 *00065 9 95 o00 o 000 0375...

A: Introduction: To make it less hard or difficult; to make it simpler or easier To condense an algebra...

Q: Choose all the correct statements about the function: y = -4 sin(3x) +5 The amplitude of the sine fu...

A: Let us consider the equation y=Asin(Bx+C)+D The amplitude of the equation is |A| The period of the e...

Q: z² + (2 + 3i)z+3 – i = 0 -

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Q: the ntegral tervals is

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Q: Consider f e C} (R") and the following function 1 Hy (æ, z) = f(z) + Vf(z)"(x – z) + ||x – z||3, 27 ...

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly rep...

Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy - 4x²y...

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Q: 10 Eu, = 6. %3D 1.3.5 for this series ...* ....... 3.5.7 5.7.9 ans.

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Q: Example 27 Find the formula for the inverse of the following functions: 2x+3 a. g(x) = x² – 1 b. h(x...

A: The inverse of a real-valued function is a map such that the composition of the original function an...

Q: (b) Consider the integral * x2 cos x dx I = x4 + 5x² + 4° -00 (1) Find the roots of z4 + 5z? + 4. (i...

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Q: 2. Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 12 in...

A: Note:- The solution for problem (2) is here as you mentioned the question number. Given that a circl...

Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the...

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Q: You buy flour in bulk for a recipe. What is the unit price of the flour based on the graph? Cost of ...

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Q: A. Find the value of x. 61 = x ( mod 7) 1. 71 = x ( mod 8) 2. 5) 89 = (x + 3) ( mod 4) 78 + x = 3 ( ...

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Q: Consider the differential equation dy/dx = 3 - y. (a) Elther by inspection or by the concept that y ...

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Q: Three forces P, Q, R act along the sides of the triangle formed by the lines x + y = 1, y -x%-1, y =...

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Q: [C.] 1. A hungry cat is noisy. If a hungry cat is noisy, then the dogs bark. Either the dogs bark or...

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Q: Consider the system: x ̇ = 4x(1+y) y ̇ = −y+2(x2+y2) Contruct the operator and identify A,g in re...

A: This is a question of system of nonlinear differential equation.

Q: . Consider the function f(t) = 2t² – 3t + 7 on the interval –1 <t < 1 with periodicity P = 2 Give a ...

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Q: 1. Define x*y over R\ {-1}by x*y = x + y +xy. Prove that this structure forms an abelian group.

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Q: What is 6 times 67

A: There is no such introduction for the solution.I have explained it within the solution.Please go thr...