2t 6. Let H be the set of all vectors Show that H is a subspace of R³. What is the -t dimension of H?

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

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Q: Let S = i. ii. iv. [2s- - S s,te R t Inter} -S Show that S is a subspace of R4 Find two vectors that…

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Q: Let H be the set of points inside and on the unit circle in the xy-plane. That is, let {{]***a :x² +…

A: According to the given information, H be the set of points inside and on the unit circle in the x-y…

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: Find the orthogonal projection ŷ of the vector y = onto the subspace W = -7 Span u =

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Q: /hat is the dimension of the subspace W = {A= [a¡j] € R5×2|a52 = 0}?

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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 A = { | 2.x |x € R}. Is A a subspace of R³? З Let B x + y + z = 0}. Is B a subspace of R³?

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Q: -2 Find the orthogonal projection ŷ of y = 3 onto the subspace 2 -2 W = Span { u , U2 Ex: 1.23 : ||

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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 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: Let S be the subspace of R2 spanned by e1 and let T be the subspace of R2 spanned by e2. Is S ∪ T a…

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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: a Q#01:- Let W be the set of all vectors in R3 of the form where a and La + b! b are any real…

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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: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

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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: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y? + z²) = 0. Is V a subspace of R?

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Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5

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Q: 16. Let V be the set of vectors (x, y, z) E R³ such that r(y?+ z²) = 0. Is V a subspace of R³?

A: Test for subspace for V to be a subspace  If u and v are elements of v then u +av must be in V where…

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: 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 distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.

Q: 12. Let K C R" and let V = { E R" : a1y Vy E K}. Prove that V is a subspace of R".

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: 4 6' Let S be the subspace of R° spanned by the vectors and and let b = 3 Find the point in 4 S that…

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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: What is the dimension of w = {A € M2x2 (R) : A"| =ö} ĄT -2 1 2 This is not a subspace

A: W=AEM2×2(R) : AT1-2=→0  Let A=abcd, a,b,c,dER     AT=acbd     AT1-2=→0  ⇒acbd 1-2 =00 ⇒a-2cb-2d=00…

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

A: solution is given below

Q: -4 Find the orthogonal projection ŷ of y onto the subspace 4 W = Span { u1 -5 Uj = u2 Ex: 1.23 : ŷ =…

A: Given

Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

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Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: S= {[a b c]€ R³|a = b+ 1} is a subspace of R. %3D صواب İbi

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Q: . Let u = 6 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: W y x+ y+z = 0 is a subspace of R³. Select one: True False II

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Q: II. Decide which of the following are subspaces of corresponding vector spaces: C R?

A: Vector space.

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

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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: W e R"|2, > 0 over the field of reals is a subspace of the specified vector space ER"

A: Given that W=x1x2x3⋮xm∈Rm|x1≥0 and V=x1x2x3⋮xm∈Rm The objective is to show that W is subspace of V.…

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 y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

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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: For a certain subspace W, the orthogonal projection of the vector y = 5 onto W 4 is ŷ = |1. Use this…

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Q: Let W = 2c = b = –3d} be a subspace of M22. a Then dimension of W is equal to: 3 4 None of the…

A: We can solve this as follows:

Q: Let V - P2 be the vector space of polynomials of degree at most 2, and let H be the span of the…

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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: 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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