O Show that whether the functions sint and cost in the vector space C[-n, 7]of continuous functions on the closed interval [-7, n]are orthogonal or not?

Q: Let C be the straight line segment in the xy-plane from the point (1, 2) to the point (5, 3). Let F…

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Q: Consider inner-product = | f(x) g(x) dx defined for vector space C[-1, 1], then for the function…

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Q: Show that the vectors (3+ /2,1+V2) and (7, 1 +2\/2) in R² are linear!ly dependent over R but…

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Q: 2.52 Prove that Ca, b] is a vector space.

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Q: If (a, b) is a local maximum of f, then D, f(a, b) = 0 for any unit vector u e R?. True False

A: Question: if (a,b) is a local maximum of f, then Du→f(a,b)=0 for any unit vector u→∈R2.

Q: Let V be the vector space of differentiable functions on 0, 1| with continuous derivative. Which…

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Q: Q4) Let V be a vector space over F. Let a E F and v E V satisfy the equation av = 0. Prove that…

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Q: 12. Show that the set of all continuous function on the interval [-1,1] is a vector space under…

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Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

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Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

Q: Let V = {(x, y): x 20) with standard operation on R2. Is V a vector space?

A: Given set is  V={(x,y):x=>0 }

Q: Q6: Show that R³ = {(x1,x2, x3)|lx1,x2, x3 E R} is a vector space

A: Vector space is the field created by set of vectors with specified direction and magnitude, usually…

Q: 7. Let C[-7,7] be the vector space of continuous function over [-n, 1] with an inner product 1 (5,9)…

A: C-π,π is a vector space of continuous function, with inner product <f,g>=1π∫-ππfxgxdx show…

Q: The dimension of the vector space R' is equal to 8. Select one: O True O False

A: Since the dimension of the vector space Rn is n. Because, Rn has n-tuple elements.

Q: Determine the dimension of the vector space. R9

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Q: Find the boundary of the sequence xn in the normalized vector space C [a, b], if it exists. 4 cos 3…

A: The given sequence is: xnt=4cosn3t5+cosnt a=-5π, b=-4π

Q: Let V ((x,y): x 20) with standard operation on R2. Is V a vector space?

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Q: Use the inner product (f, 9) = | f(x)g(x) dr %3D in the vector space CU[0, 1] of continuous…

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Q: Use the inner product (f,9) = f(z)g(x) dz in the vector space C"0, 1] of continuous functions on the…

A: It is given that fx=-5x2-3 and gx=9x-7. We have to evaluate f, g, f, g and αf, g where αf, g is the…

Q: Consider inner-product = ] f(x)g(x) dx defined for vector space C[-1, 1] , then for the -1 function…

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Q: Find the boundary of the sequence xn in the normalized vector space C [a, b], if it exists. 4 cos/3…

A: Solution: Here the sequence is xnt=4cosn3t5+cosnt and a=-5π,  b=-4π

Q: If r(t) is a vector-valued function that is continuous on the interval [a, b), then r(t) dt is a…

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Q: Determine the dimension of the vector space. R5

A: If V is a part of a finite set, then V is said to be finite-dimensional, and the dimension of V,…

Q: Show that V={(x,2020x): x in R} is a vector space

A: According to the given information, it is required to show that the given set is a vector space.

Q: FBShow that these vectors (taken from a vector space consisting of all functions of the real…

A: The objective is to show that the vectors of the given set are not linearly independent.

Q: Let V = {(x, y): x 20} with standard operation on R². Is V a vector %3D space?

A: Our objective is to conclude V is a vector space or not.

Q: 21 Determine the domains of the vector-valued function r2(1) = (v/8 – 13, In 1, eviy %3D -

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Q: b) Let V be the F-vector space of F-v

A: Given, V be the F-vector sequences ann≥0. For each i≥0, let δi be the sequence whose ith is 1, and…

Q: Consider inner-product = | f(x)g(x) dx defined for vector space C[-1, 1] , -1 then for the function…

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Q: Consider the vector space V = P over the field of real numbers F = R. Is the vector 4 – x – x 2 in…

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Q: Let V = {(x, y): x 20} with standard operation on R2. Is V a vector space?

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Q: Let V = {(x,y) where y= 3x+1 x ER} with scalar multiplication defined by k(x,y)=(kx,y) is a vector…

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Q: In the vector space of all real valued functions, find O (1+cos 2t, cost sint, cos² t) O (sin 2t, 1+…

A: Given spanning set is sin 2t, 1 + cos 2t, cos t sin t, cos2 t

Q: Let V be n-dimensional vector space over c en for any n scalars ₁, ... , E F there-

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Q: Let P denote the set of all functions f on [0, 1] such that there exists at least one point x E [0,…

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Q: Show that ℝ2 is a vector space with usual addition and multiplication.

A: To prove that R2 is vector space we have to prove following; 1. R2 is abelian group under addition.…

Q: If f(x) and g(x) have a period p, show that h(x)3Da f(x) + b g(x) (a, b constants) has the period p.…

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Q: 2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y?…

A: TO solve the question, we use the following facts (a) A functions is differentiable at a point if…

Q: Let V be an n-dimensional vector space. Define f : V \rightarrow \R by f(v) = |v2|. Let p,q \in V.…

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Q: Let f1(x) = 3x and f2(x) = ∣x∣. Graph both functions on the interval −2 ≤ x ≤ 2. Show that these…

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Q: Consider inner-product = | f(x) g(x) dx defined for vector space C[-1, 1] , then for the function…

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Q: Consider inner-product = | f(x) g(x) dx defined for vector space C[-1, 1] , then for the function…

A: The solution is given as

Q: What is the dimension of the vector space R

A: The objective is to find the dimension of the vector space R5.

Q: Let F(x, y) = (5x², 2y ). Compute the flux 6 Fnds of F across the boundary of the triangle with…

A: The given vector field is Fx,y=5x2, 2y2. The given region R is the triangle with vertices 0, 0, 2,…

Q: The set R2 is a vector space over R. How Prove it ?

A: We need to check each and every axiom of a vector space to know that it is in fact a vector…

Q: Use the inner product 1 (f, 8) = f(x)g(x) dx in the vector space CO[0, 1] of continuous functions on…

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Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 3tk O 5 5 5 k k 2 -2 5 Z 2…

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Q: If T and H are invertible linear operators on a vector space V(F), then show that TH is invertible…

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Q: 1) Verify that d/dx(fg) is a vector space over R, or explain why it is not.

A: The objective is to find whether the ddxf.g is a vector space over ℝ. Since it is known that…

Q: Let f : R" → R" be a function with the property that for any v, w E R" it holds that f(v) · f(w) = v…

A: Given the function f:ℝn→ℝn. Given that, this function preserves the operation 'inner product'. Which…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.