In the vector space of all real-valued functions, find a basis for the subspace spanned by {sin t, sin 2t, sin t cos t}.

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: Let W be the subspace of IRª spanned by the vectors 4 2 and -1 Find the matrix A of the orthogonal…

A: Consider the given information: Let W be the subspace of ℝ4 spanned by vectors :1-11-1,4-2-1-7 To…

Q: .

A: Here we have to find an orthonormal basis for the subspace spanned by 1, x, x2:

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: We first write given vectors is matrix form and then reduce the given matrix in row echelon form.…

Q: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

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Q: If V is the vector space of real valued continuous functions , then show that the set W of all d’y…

A: Our Aim is to show that the set W of all solutions of the differential equation3d2ydx2-5dydx+7y=0…

Q: Find the projection of the vector v onto the subspace S. S = span

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Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: 2 Find the orthogonal projection of u = 1 onto the subspace of R3 spanned by the vectors -3 - 2 V1 =…

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Q: 6. Let C"(R) denote the sct of all real-valued functions defined on the real line that have a…

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Q: Find a basis of the subspace of R" that consists of all vectors perpendicular to both 1 and 1 -5 5…

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Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

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Q: Find the orthogonal projection of the vector v onto the subspace S. v = |2 S =

A: projS(V) = (u1.v/u1.u1)u1 + (u2.v/u2.u2)u2

Q: In the vector space of functions f: R → R, find a basis for the subspace spanned by {sin t, sin 2t ,…

A: Solving question by theorem vector space

Q: {{},} Let W be the subspace of R3 spanned by write j = |3 3 as the sum of a vector in W and a vector…

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

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Q: 26. In the vector space of all real-valued functions, find a basis for the subspace spanned by {sin…

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Q: Let W = {a + bx + cx² + dx³| c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to

A: As given W be a subspace of P3.

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: if a vector space is the set of real valued continuous functions over R , then show that the set W…

A: Given V is a vector space of all continuous functions over ℝ. W is a set of differential equation…

Q: In the vector space of all real-valued functions, find a basis for the subspace spanned by {sin…

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Q: Let W be the subspace of the space of all continuous real- valued functions spanned by {cos2 t,sin2…

A: let U= cos2t,sin2t,cos2t and W be the subspace of all continuous real-valued functions spanned by…

Q: Let H be the subspace of R with basis B = 3. and let x = 10 6. Is xa vector in H? 14 fx is in H,…

A: Given H is a subspace of R3 with basis {204,231}And x=10614To check x is in H

Q: snip

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Q: Let W be the set of all vectors of the form Na subspace of R³ 0 2

A: Here given that  vector  [a 0 2]    We know that condition of subspace  w is zero vector belong…

Q: Let W be the set of all the vectors of the form y where x and y are any real numbers. 2х-Зу…

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Q: 4. Consider C" as a real vector space. It has a subspace U := C x {0}"-1. What is the dimension of…

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Q: a Is the set of vectors of the form La+2b] subspace of R3? Show your proof. a

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Q: Let H be the subspace of R with basis B -2 and let x 6. (:) Is x a vector in H? 9. If x is in H,…

A: Given basis is B

Q: Find the projection matrix P that projects vectors in R onto W Let W be the subspace of R spanned by…

A: The inverse of a 2×2 matrix is calculated using the formula: a  b c  d -1=1deta  b c  d d  -b -c  a…

Q: Let H be the set of all vectors of the form 3s . Find a vector v in R3 such that H = Span {v}. Why…

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Q: snip

A: We can represent the given set again as: W=xyz:x=3y+1 and z=-2y Let  w1=x1y1z1∈WThen,x1=3y1+1 and…

Q: snip snip

A: Consider the set S=x,y| xy⩾0. Note that 1, 2,  -2, -1∈S. Because it satisfies 1·2≥0   and   -2·-1≥0.…

Q: Is the set of functions (taken from a vector space consisting of all functions of the real numbers):…

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Q: Let W = { |xy <0}. Is W a subspace of R?? If so, use generic terms to demonstrate the necessary…

A: W is not a subspace of R2.

Q: Denote by C[0, 1] , the space of all continuous functions defined on the unit interval [0, 1]. Show…

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Q: Find the orthogonal projection of V = onto the subspace W of R' spanned by U1 = , U2 Uz = VW ||

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Q: ) The degree of pa is equal to the dimension of the cyclic subspace Z (a ; T) .

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Q: Find the distance from the point x = (1, 5, –4) of R³ to the subspace W consisting of all vectors of…

A: First we will find out the orthogonal basis for the subspace W. Then we calculate the orthogonal…

Q: Find the orthogonal projection ŷ of the vector y = onto the subspace W = Span u 2 Ex: 5 C ŷ = %3D

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Q: Find the orthogonal projection ŷ of y = 3 onto the subspace W = Span { u1 = , U2 = 3 Ex: 1.23 %3D

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Q: Let W = (a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of Py. Then the dimension of W is equal to

A: Here we will find out dimension of W.

Q: If W is a subspace of the vector space V = R, then the vector zero belongs to W: Select one: O True

A: A subset W of a vector space V is called a subspace of V if W is itself a vector space under the…

Q: {{} } 5. Let W be the subspace of R³ spanned by write j= |3 as the sum of a vector in W and a vector…

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Q: Find the orthogonal projection of onto the subspace W of Rª spanned by 1 projw (v)

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Q: The subspace V of R4 is spanned by the vecto (a) Use the Gram-Schmidt process to find a

A: Here, in the question there is given some of the vectors with a subspace spanned by the vectors. We…

Q: Show that the set of vectors of the form a +b forms a subspace of R³. Find a 2а — b basis for this…

A: Given set of vectors of the form: aa+b2a-b Let v1=a1a1+b12a1-b1 and v2=a2a2+b22a2-b2 be two…

Q: Find the projection of the vector v = [1 0 −2]T onto the subspace

A: We have to find the projection of the vector v=10-2 onto the subspace S=Span0-11,011

Q: x=y=z

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