What is the dimension of the subspace H of R spanned by the given ved V1, V2 and v3 2 3 Vị = -8 V2 = -7 V3 4 1 ||

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0}

A: Given, W=x,y,z:x+y+z=0 Let, 2,-1,1∈W Let, -1∈F

Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: _. Let u = 6 " and let W be the set of all x in R3 such that u x = 0. (a) Show that W is a subspace…

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Q: (c) Find a subspace U such that R³ = W₁ OU.

A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.

Q: (a) find the orthogonal complement S⊥, and (b) find the direct sum S⊕S⊥. S is the subspace of R3…

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Q: Let W = {a + bx + cx² + dx°|c - 3d = 0} be a subspace of Pa. Then the dimension of W is equal to 3.…

A: PnF is set of all polynomials of degree nand smaller . PnF denotes the vector space over field F…

Q: What is the dimensionality of the subspace spanned by V = \v +7w for the following v, w? a) b) d) 12

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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: Find the orthogonal projection ŷ of y = onto the subspace W = Span { uị u2 5 Ex: 1.23 : ŷ =

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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: Show that S = {(x, Y, z)|4x – y + 5z = 0, x, y, z E R} is a subspace of R³.

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Q: Let S be the subspace of Rn spanned by the vectors x1, x2, . . . , xk. Show that y ∈ S⊥ if and only…

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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: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31…

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: The set R' of all column vectors of length three, with real entries, is a vector space. Determine…

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Q: Let W = (a + bx + cx? + dx³la + 2c 0 andb-d D 0) be a subspace of P,. %3D Then dimension of W is…

A: Given  W={a+bx+cx2+dx3| a+2c=0 and b-d=0}Since a+2c=0⇒a=-2cand b-d=0⇒b=dwhich gives…

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: For subspaces V & V-of R and V #R³, consider the set S=Vuv+. Is S=R°?

A: solution is given below

Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

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: 3) Explain why S, = {(x, y) E R²:y > 0} and S1 = {(x, x²): x E R} are not subspaces of R?. %3D

A: We will solve both these parts using only basic knowledge of subspaces and vector spaces (in clear…

Q: What is the dimension of the subspace H of R? spanned by 2 -4 4 32- :? -5 10 -10 O A) 0 O B) 3 O ) 4…

A: The number of vectors in a basis of a vector space is said to be the dimension of that vector space…

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

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Q: Is W = ((x,y) | xy=0} a subspace of R??

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R?. %3D

A: Consider the given set. U=x,-x|xinR Let, consider that, f,g∈V And f, and g is defined as.…

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: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…

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Q: Let W = {(" ):a+ 2c = 0 andb-d 0} be a subspace of M22. %3D Then dimension of W is equal to: O 1…

A: The solution is given in the next step.

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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: What is the dimensionality of the subspace spanned by V = Av +yw for the following v, w? 2 4 a) b)…

A: See the attachment

Q: Is Y = (x,y,z) | y=z} a subspace of R?

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Q: 4. Consider the vector space RR of functions f: R R. Let U = {f: R → R: f(42)=0}. Show that U is a…

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Q: Find the closest point to y in the subspace W spanned by u, and u2. 7 2 y = 21 u1 2 , u2* 3 38 - 1 4…

A: Given that     y = (7,21,38) , u1 = (2,2,-1) and u2 = (-1,3,4) Here we have to find the closest…

Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

Q: 10. Find the dimension of the subspace V span{v1, v2, V3, v4} in R³ where vi 1 V2 = , V3 = and v4 =

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Q: (A) Let U1, U2, U3 be subspaces of M2x2(R). If V = U1 e U2 e U3, then dim V = 4.

A: So,  V is the direct sum of the subspaces U1, U2, U3  of M2×2(R) , i.e. dim(U1) = dim(U2) = dim(U3)…

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: Is Q = {(x,y,z) | x=2y & z=1} a subspace of R?

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Q: Let U and WW denote subspaces of R", and assume that U C W. If dim U = n - 1, show that either W =…

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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: Show that U = {(r, y, z): r.ye R} is a subspace of R³. Then, find a linear complemen

A: Here a subset of ℝ3 is given as U=x, y, x: x,y∈ℝ

Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

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Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

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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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Q: What is the dimension of the subspace below? w = sp { J. C a) O 0 b) c)O 2 d) O 3 e) O -1 1,

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