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

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 X = 1 ,and let V = {A E M2(R) | AX = XA}, a subspace of M2(R). 0. Find a basis for V, and write…

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Q: Suppose U and W are subspaces of V such that dimU=4, dimW=5, and dimV=7. Find the possible…

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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: -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: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

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: 1 -1 Find the distance from y to the subspace spanned by u. U= y= NO N1

A: Here given vectors are: u=2021y=1-11-1

Q: Find the orthogonal projection ŷ of y: 6 onto the subspace W = Span { ui u2 Ex: 1.23 ||

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Q: Find the subspace spanned by the three vectors [2 3 1]T, [2 1-5]T, and [2 4 4]T Feuth

A: We will check the  vectors that it is linearly dependent or linearly independent.  If the vectors…

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: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

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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: (1) Suppose U and W are both five-dimensional subspaces of R°. Prove that UnW + {0}.

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Q: Find the orthogonal projection of -5 -1 16 onto the subspace W of IR³ spanned by 4 -4 and 2 24 projw…

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

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Q: 5.) Find the dimension of the subspace of Rª spanned by 5 10 , and 15

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

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Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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

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Q: If u and v are vectors in R and W is a subspace of R with (u + V) belong to W, then both u and v…

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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: 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: 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: 1 1 onto the subspace W = Span -7 Find the orthogonal projection ŷ of the vector y = u = 2 Ex: 5

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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: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…

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Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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Q: Find the orthogonal projection of -13] 15 onto the subspace W of R4 spanned by 4 and 5 -2 -2…

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Q: Let S = {" E M2xzi a = d and b+c 0 be a subspace of M2x2. %3D Then the dimension of S is equal to: 4…

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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

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: Let U and W be subspaces of R³ for which dimU=1, dimW=2, and UgW. Show that R=UOW.

A: I have shown all the conditions of direct sum of two subspaces

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: and uz = Find the closest point to y = in the subspace W spanned by u1 = The closest point is

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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: 1. Decide if the following subsets W C V are vector subspaces or not (justify) (a) W = x €RCR?. COs…

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

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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: 2 Find the dimension of the subspace H of R spanned by – 12 8 ..... dim H =

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Q: Let S= +c = 0 be a subspace of Mzxa- Then the dimension of S is equal to: 2.

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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: 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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