5.4) (6)  Find the projection of the vector v onto the subspace S. S = span 0 1 1 , 1 1 0 v = 3 4 2 projs v = ??

Q: -4 Find the orthogonal projection ŷ of y = 4 onto the subspace 3 -3 W = Span { uj U2 = 2 Ex: 1.23

A: With the help of definition of projection of a vector on a subspace, we solve this problem.

Q: 3. Decide if the followin Let V and W be vector subspace of V.

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Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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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: 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: 5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal…

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Q: Find a basis for the subspace of R3 spanned by s. S = {(1, 5, 9), (-1, 6, 9), (2, 6, 1)}

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Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 2, 6), (-1, 3, 6), (2, 3, 1)}

A: The given subspace is: S= (1, 2, 6), (-1, 3, 6), (2, 3, 1)

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: Find the projection of the vector v onto the subspace S. 8. 4 S span 23/2 9. projs V = 11/2

A: Find the projection of vector V.

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. Find a basis for the subspace spanned by the given vectors. What is the dimension of the…

A: Given vectors  1-32-4,-39-612,2-142,-45-37 we have to find    (a) Basis for the subspace spanned by…

Q: 4 Let S be the subspace of R* spanned by x1 = (1,0, – 2, 1)" and x2 Find a basis for S. (0, 1, 3,…

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Q: 4. Orthonormalize S (Gram-Schmidt). 5. Find the projection of v onto W.

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Q: 1 Q5. Find an orthonormal basis of the subspace spanned by the vectors

A: The solution is given as

Q: 2 -3 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = 1 %3D 8 Ex: 5…

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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: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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Q: -2 an orthonormal basis of the subspace spanned by the vectors 121C

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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 a linearly independent set of vectors that spans the same subspace of R* 4 as that spanned by…

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Q: 3. Without computing A, find bases for the four fundamental subspaces if: [1 0 0 6 1 0 9 8 [1 2 3 4…

A: Answer is mentioned below

Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: 1. Find the ortho gonal puojection of the Vector (1,3,1 on the subspace of IR? Spanned by…

A: Projection

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: Find a basis for the subspace of R³ spanned by S. S = {(1, 4, 7), (-1, 5, 7), (2, 5, 1)}

A: The matrix form the vectors is: A=1-12455771

Q: Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}

A: To find the basis for the subspace of R3 spanned by the given set of vectors S.

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

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Q: Let ū be some fixed vector in R" and let S be the set of all vectors in R" that are orthogonal to ū.…

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

A: Any linear subspace is a combination of many subspaces, these subspace may distinguish with each…

Q: 2, Find bases for the fundamental subspaces; R(A), R(A"), N(A), and N(A"), given the matrix 1 -2 2 A…

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

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Q: Is the following set of vectors in R 3 linearly dependent: {(1, 0, 3),(2, 1, -2),(0, -1, 8),(7, 2,…

A: The solution is given 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 a basis for the subspace of R' spanned by the vectors. {(1,1,0,0), (0,0,1,1), (-2,0,2,2),…

A: We have fond the maximal linearly independent subset of the given set.

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 basis for the subspace of R³ spanned by S. S= {(4,2,-1), (1,2,8), (0,1,2)}

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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: 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 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: Find a basis for the subspace of R3 spanned by S.S = {(2, 3, −1), (1, 3, −9), (0, 1, 5)}

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1,8), (7,2,…

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Q: 5. Find basis for the subspace u- of R for the vector u = orthogonal subspace of u) (1,3,-4). (Here…

A: As we know that S=v1,v2,...vk be a set of vectors in Rn  then S is called an Orthogonal if and only…

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 5, 7), (-1, 6, 7), (2, 6, 1)}

A: Write the given set of elements as the rows  to form a 3x3 matrix. The space spanned by the rows of…

Q: Consider the vector subspaces U, V  ,W ⊆ Rn such that U ⊆ V ⊆ W. If dimU = 5 and dimW = 7, what can…

A: - it always contains a set of 5  linear independent vectors (True) This statement is True. As dim V…

Q: Q2/ Find orthogomal basis for subspace generated by the basis A, = (2,2,4,4), %3D A2 = (0,1,3,5) ,…

A: To find the orthogonal basis, use Gram-Schmidt process.  uk→= vk→−∑j=1k-1proj uk→  vk→, where proj…

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

A: