Find the closest point to y in the subspace W spanned by v1 and v2 y = | 1 -3 V2 = -2 а) b) 2 c) 1 d) None of these

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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Q: Show that V is a subspace of R³: V is the set of all (x, y, z) such that z = 2x + 3y

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Q: In the vector space , with the Euclidean inner product (i.e. the dot product), consider the subspace…

A: The fourth option '2' is correct. First find the dimension of W. Write the four vectors that span W…

Q: Show that the set W : {(x, y, 5x-4y)| x and y are real numbers} is a subspace of R³.

A: We are give, W=x,y,5x-4y| x and y are real numbers To show: W is a subspace of R3 This can be done…

Q: 4) Show that the subspaces of R? are precisely {0}, R2, and all lines in R? through the origin.

A: A subspace of a vector space is itself a vector space that is contained in another vector space.

Q: Show that the solution set to a system of equations of the form a + a, x = 0 + an x = 0 a m, + ... +…

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: Find the orthogonal projection of 4 onto the subspace W of R* spanned by 1 1 -1 projw (7) =

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Q: Is W = {(x, y, z, w) | 4z – 2y = 3w – x & y+ z = -2x} a subspace? Justify your answer. If it's a…

A: Given W=x,y,z,w:4z-2y=3w-x & y+z=-2x

Q: Let W = {a + bx + cx + dx| a+ b = 0 and c – 3d = 0} be a subspace of P3 Then the dimension of W is…

A: Linear combination of vectors we use to find.

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

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Q: Find the closest point to y in the subspace W spanned by v1 and v2 1 ,V2 = 1 y = V1 = -3. I • E 2 b)…

A: Here we have to find the closest point to y in the subspace W spanned by v1 and v2 .

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

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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

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 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: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

A: Given that a) W=x,y,z|x,y,z∈ℝ,x=z+2 of ℝ3. b) W=pt-tq of M22 Check the space W is the subspace of…

Q: snip

A: We have vector space of all real numbers over real numbers And S is subspace of vector space given…

Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

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Q: ind the closest point in the subspace with the (not orthogonal) basis {b1, b2, b3} to the head of…

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Q: Find the orthogonal projection of V = nto the subspace W of R* spanned by Uj = U2 = Uz = -6/4 -6/4 w…

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Q: 2. Determine if the set S consisting of vectors of the form b where abc = 0 is a subspace of R³.…

A: No, S is not  a subsapce of ℝ3. Explanation: Here,  s1=110 and s2=001 belong to set S. Then,…

Q: Find the closest point to y in the subspace W spanned by vị and vz 2 y =| 1 ,v1 0,v2 -2 2 а) b) c)…

A: The following is the solved answer.

Q: Determine whether the set of all 3-tuples of the form (x, y, z), where z = x – 2y, form a subspace…

A: If W is a subset of a vector space V over a field F, then W is a subspace of V, only if it satisfies…

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

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Q: ind the closest point to y in the subspace W spanned by vị and v2 2 y =| 1 |,v1 = ,V2 = |-2 2 а) b)…

A: We will use the following method.

Q: Is M = {(x,y,z)|x is nonnegative} a subspace of R³? Yes or No? Justify or give/find a…

A: Given  M =  x, y, z  x is nonnegative

Q: Consider the subspace S = {(7a5b)|a,b € R} Then the dimension of S corresponds to?

A:

Q: 9. Find the vector closest to y from the subspace of Rª spanned by Vị and v2. 3 1 Vị = 1 , y = V2 =…

A: To find  The vector closest to you from the subspace of R^4 spanned by v1 and v2.

Q: Q. Show that (a,b,c) where c=a+b is subspace of R

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Q: projw(x) is not orthogonal to every vector in the subspace W. O True False

A: We have to check whether the given statement, "projwx is not orthogonal to every vector in the…

Q: Let W = {(" ):a = 2c = b = –3d} be a subspace of M22. Then dimension of W is equal to: None of the…

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Q: Find the orthogonal projection ŷ of y = 6 onto the subspace 2 -3 W = Span { ui = 3 Ex: 1.23

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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: Consider the set S = y ER : 3x – 5y = 0, x + z =- . Is this a subspace of R ? Explain why or why…

A: Given set is S=xyz∈R3:3x−5y=0, x+z=4. We have to check whether the set S is the subspace of R3 or…

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = eܐ ܝܕ ܝܐ [19 12 1…

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Q: Find the orthogonal projection of onto the subspace W of Rª spanned by projw() = v= 4 -2 -13] 3 15…

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

A:

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

A: Determine the dimension of the subspace of ℝ3 spanned by the given vectors.

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

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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: Show that points on the plane x-2y+4z=0 form a subspace of R3

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Q: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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Q: x=y=z

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Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors u;. are orthogonal.)…

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Q: Find the closest point to y in the subspace W spanned by vị and vz 2 1 y =| 1 |,v1 =| 0 [0] 2 lo] 2…

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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.