Find the orthogonal decomposition of v with respect to the subspace W. (That is, write v as w + u with w in W and u in w-.) 3 3 V = -3 W = span 4 1 1 -1/9 1/9 W = 2/9 28/9 -28/9 u = -1/9

Q: (2) Find a basis for the subspace W = {(a+c,2a – 6, 3a – 26 – c, b + 2c) | a, b, c E R} of R4

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A: Let us consider set S then the set S is  linearly independent or dependent  Determine the linear…

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A: Let A and B be any two members of W. Then AT = - A, and BT = - B.

Q: let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given…

A: S forms a subspace of R2

Q: 4. Find an orthogonal basis of the subspace W of R5 spanned by {ū₁ = (1, 1, 1, 0, 1), 2 = (1, 0, 0,…

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Q: Find the standard matrix of the orthogonal projection onto the subspace W. Then use this matrix to…

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

A: NOTE: Refresh your page if you can't see any equations. . write all 4 given vectors in the matrix A

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A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: Find a basis for the subspace of P2 spanned by the given vectors.  1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

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A: We will reduce the dependence of the set by checking if (and how many) any vectors are dependent on…

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Q: Let W be the subspace of vectors in R3 that are orthogonal to w = (-1, 1, 1).  Find a basis for W.…

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Q: The given vectors form a basis for a subspace W of R3 or R4. Apply the Gram-Schmidt Process to…

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Q: Find a basis for each subspace... [5r-3s, 2r, 0, -4s] ER^4:r and s are scalars

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Q: Let W be the subspace of all symmetric matrices in M2,2. What is the dimension of W?

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Q: Find the standard matrix of the orthogonal projection onto the subspace W. Then use this matrix to…

A: Given: To find: Standard matrix for orthogonal projection onto the subspace W and then use this…

Q: Find a basis for the given subspace of R , and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

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Q: 3 Find a basis of the subspace of R' defined by the equation -7x1 – 5x2 – 4x3 = 0.

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Q: For vectors, v0= (0,3,4,2),v1= (1,1,2,1), v2= (1,0,0,0), v3= (0,0,1,0), find an orthonormal basis,…

A: Solution by using Gram Schmidt process as follows :

Q: Let W be the set of all 3 x 3 matrices whose trace is zero. Show that S is a subspace of M33.

A: Let W be the set of all 3×3 matrices whose trace is zero. Show that W is a subspace of M33.

Q: Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.

A: Given that, -3x+2y+5z=0

Q: Consider the set U2 : a, b, d e R} of 2 x 2 upper triangular matrices with real number entries.…

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Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

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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: 3 Find a basis of the subspace of R’ defined by the equation -5x1 – 7x2 – 2x3 = 0.

A: Consider the given equation:

Q: Apply the Gram-Schmidt process to find an orthogonal basis for the given subspace. -1 S = span 1 2 1

A: Given a subspace S.    S=span-101,341,416 Find an orthogonal basis for S by using Gram-Schmidt…

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Q: Find a basis of the subspace of R defined by the equation 6y, + 3y, – 4y, = 0 Basis:

A: Given data÷

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Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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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: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

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Q: Find a basis for the given subspace of R°, and state its dimension for the plane 3 x- 2 y+ 5 z = 0.…

A: We have the vector space R3 , the subspace here is: W={(x,y,z) | 3x-2y+5z=0 ; x, y, z∈R}

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

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Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

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Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

Q: -2 , find the closest point to v in the subspace W spanned by -2 Given v =

A: Introduction: Th formula for the projection of vector w on v is given by,…

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Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: Find a basis for the following subspace of R°: W3D {(aj + 5а2 — 2а3, 2а1+ 6а2 — аз, Зај + 7а2) : ај,…

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Q: Let W be the subspace of M10,10 (i.e., 10 × 10 matrices) consisting of all matrices whose diagonal…

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Q: Find a basis for the subspace and state the dimension. p– 2q 2р-5r :P,q,r e R а. -2q +2r -Зр+ 6r| 1…

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Q: 6. a. Give a basis for the orthogonal complement of the subspace V C R' given by V = {x € R* : xị…

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Q: Find a basis for the subspace W of R³ orthogonal to {(1,1,3, 4, 1), (1, 2, 1, 2, 1)}.

A: We Use Gram Schmidt Process to Find Orthogonal basis. Use Standard Inner product as <(u1, u2),…

Q: Consider the subspaces U = span{[1 -4 -5],[-1 –6 -13]} and W = span{[4 -4 4],[-2 0 -2]} of V = R'x3.…

A: Any vector belongs to a space spanned by v1 and v2 is the linear combination of v1 and v2.

Q: Consider the subspaces U = span{[3 -3 1],[12 3 -7]} and W = span{[-3 2 0],[1 8 -6]} of V = R1x3.…

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Q: Consider the subspaces U = span{[3 5 0],[0 12 -6]} and W = span{[–3 2 -1],[-15 7 -11]} of V = RIX3.…

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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.