Problem 1 Consider the vector space C² V = 2 2+3i and w= (7+21) 7+4i {(W) : w, z = C} over the field C of complex numbers. Check if are parallel or not. Explain.

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

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A: Note : Since you have posted a question with multiple subparts, we will provide the solution only to…

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: State the main idea for the Newton form of the basis?

A: Let there is a polynomial.  The polynomials of Newton’s basis are defined as:

Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

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Q: Use complex numbers to transform the following vectors, rotating by the angle and scaling by the…

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Q: 3. Describe all solutions of Ax - A = 0 in parametric vector form, where 1 0 0 0 -4 -2 0 3 -5] 0 1…

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Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

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Q: Describe all solutions of Ax = b, where [2-5 3] A= -2 6-5 and b = -4 7 0 2 19 Describe the general…

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Q: Let a = (5, 4) and b = (5, – 8). Compute the dot product. a b

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Q: Solve the problem. Describe all solutions of Ax = b, where 2-5 31 A= = [] = [] -2 6-5 and b 4 7 0,…

A: Given: A=2-53-26-5-470 and b=-38-9. To Do: Describe the general solution in parametric vector form.

Q: 5. To solve the initial value problem dy t + y(t) = t sint, t> 0 y2) = 1, dt a. Find the…

A: Given,

Q: Let u = 10i + 2j, v=i+j, and w = i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Describe all solutions to Ax = 0 in parametric vector form for 1 -3 2 0 5 A - 00 00 1 2 0 -1 000 1 0…

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Q: 10 The complex numbers V and W represent two force vectors. Place them on an Argand diagram and…

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Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

A:

Q: Use the dot product to determine whether v = 2i + 8j and w = 4i - j are orthogonal.

A: Given: v=2i+8jw=4i-j