2 Find the orthogonal projection of u = 1 onto the subspace of R3 spanned by the vectors -3 - 2 V1 = , V2 = 1 -2

Q: Find the projection of the vector v onto the subspace S. S = span 1 %3D V = 1 -1 1

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Q: Find the dimension of the subspace H of IR2 spanned by the vectors and

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Q: 4.) Determine the dimension of thr subspace of M21 consisting of vectors of the form [a – 2b] a + b…

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Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: Find the orthogonal projection of u on the subspace of R³ spanned by the vectors v₁ and v₂. u = (1,…

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

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Q: Find the standard matrix for the orthogonal projection of R3 onto the subspace spanned by aj=(1,1)…

A: The vectors that span the subspace are a1=1, 1 and a2=0, 1. The normalising vectors are 12, 12 and…

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: 9. Find the orthogonal projection y of y = onto the subspace 2 0. W Span u = -3

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Q: Find the orthogonal complement S⊥ of the subspace S of R3 spanned by the two column vectors of the…

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Q: dimension

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

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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: [5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =

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Q: 1 2 Find a basis for subspace V of R4 spanned by the vectors 3 dimension of V? 8 What is the

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Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

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Q: Find the projection of the vector v onto the subspace S. 1 1 1 S = span 1 v = projs v =

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Q: Find a basis for the subspace of R, the plane 2x +y-z+ 3w-0 and convert it into an orthonormal ban

A: Given the subspace 2x+y-z+3w=0. To get the orthonormal basis. The formula for orthonormal basis is,…

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: 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: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: Find a basis for the subspace of R" spanned by the vectors 1 1 .2. -3. .6.

A: Use the given vectors.

Q: The span of a set of vectors from a vector space V is a subspace of V. true or false?

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

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

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

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: Find a basis for the subspace of R3 spanned by S = {v1, v2, v3} = {(−1, 2, 5), (3, 0, 3), (5, 1,…

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

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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: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: 6. The projection of 12 onto the subspace of R spanned by ĝ V2 and a, 1 equals: -6 1,

A: 1. Let S be a non-trivial subspace of a vector space V and assume that v is a vector in V that does…

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

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

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Q: Find the orthogonal projection of 10 onto the subspace W of R° spanned by 9. and 3 -1-10 3 projw (i)…

A: To find  The orthogonal projection of v onto the subspace of W spanned by the given vectors.

Q: .Is the set of all vectors of the form b. where a and b are any real numbers, a subspace W of R?…

A: Yes, W is a subspace of R^3.

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: 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 of u = 1 onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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

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Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the 1 2 2 - 1…

A: We have to solve given problem:

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

A: Given:   v = 123 , u1 = 2-21 , u2 = -114    Also, given that the subspace W is spanned by the…

Q: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.

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

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