Use Stokes theorem to evaluate V × F · dS over the surface of the paraboloid z = 5 – x² – y? above the plane z = 1, where - F = (y – 32) i+ (x² – 42) j+ (x + 3y) k %3D Hint: Stokes' theorem S Ss V × F · dS = ScF•dR. What is C in this case? 5.

Q: Draw the vector to show: (а) (b) (c)

A: A→ = AxAy , This is the representation of vector in matrix form. These type of matrices are called…

Q: 'S' is a collection of vectors. Show that the rank of S is equal to the dimension of Span(S). Please…

A: Let  is a collection of vectors. Now, let the rank of is equal to  (say).It's row reduced eschelon…

Q: 1 3. Find the coordinate Vector [x]3 of the vector x = relative to the given basis B. 1 3 B = -4

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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: What is the least number of linearly independent vectors needed to span a line? [Enter a whole…

A:

Q: Please prove mathematically that when y=0, the defined set C is not a subset.  Why is the vector…

A: The given sets are:

Q: Explain why there is no vector v such that × v =.

A: We explain why there is no vector v such that  <1,2,1> × v =<3,1,5>

Q: x + y 2x + y. 2 -4_ x = Ex: 5 : Y= Ex: 5

A:

Q: Let <··· Give the B-coordinate vector for each of the following: (a) B = H ²21 (b) 2 (c) H

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Q: discuss the directional vectors (gradient and curl) with physical examples.

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Q: Compare between zero vector and unit vectors with drawing the suitable curves.

A: Solution : Here we have show the difference between the Zero vector and Unit vector.   Concept : A…

Q: Solve the problem. Describe all solutions of Ax = b, where []· Describe the general solution in…

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Q: The first problem is Question 4: vector is described. Express the vector in terms of i and j. A…

A:

Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: A velocity vector of variable magnitude of an object can have a constant direction. O True False

A:

Q: What is the effect of scaling a Vector? Give an example?

A: we need to explain the scaling of vector. and we  need to give an example. First let us define what…

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: Explain how you would convert from a plane's scalar equation to a vecto

A: Lets understand the process of converting scalar equation of a plane to vector equation by an…

Q: What is the shortest distance d from the line L₁ defined by the vector equation to the line L₂…

A: Consider 2 lines in vector form as: v1 = a1 + c * b v2 = a2 + d * b here, c and d are the constants.…

Q: You know that vectors show not only magnitudes, but directions as well. Explain how vector functions…

A: we know that vectors show not only magnitudes, but direction as well. we have to explain how vector…

Q: De termine if the vectors 2 re lincarly independent or linearly dependent Please explain your answer

A:

Q: Find the least squares regression line, using the matrix form for linear regression. (−7, 1), (1,…

A: The linear relationship between two variables x and y can be defined using the equation, y=b+mx. The…

Q: 5 Aaron and Maya want to write the vector u = -5 as a linear comb -19 -2 1 V1 -2 V2 = 1 and V3 = 2…

A: The { v1 ,v2 ,v3 } is not a set of orthogonal vectors.

Q: Give one example to illustrate that vectors satisfy the triangle inequality. Justify your answer

A: Vectors of Triangle Inequality : u+ v≤u + v

Q: Dot Product Find the dot product of the vectors a = (1, 3, −4) and b = (–2,3,1)

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Q: A bike trail is drawn on a coordinate system. Each end of the trail is an x-intercept. The height of…

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Q: Are the following vectors linearly independent? Do they span R³? Justify your answers. ECHE 3 2

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Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.