Find the orthogonal projection of - -1 1 12 2 || subspace W of R4 spanned by -1 1 1 = 0 7 0 1 1 " −1 -1

Q: Find the Kernel and Range of the linear transformation L : R^3 → R^3 defined by L(x) = (x3, 0,…

A: In linear algebra, the kernel of a linear transformation is also known as the "null space." Given a…

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: 4. Let W be the subspace of R³ spanned by w the orthogonal projection of 8- onto W. - (2/3) 1/3 and…

A: orthonormal vectors:- A set of non zero vectors v1, v2, v3,......, vn is called orthonormal if…

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw() = 4 6 V= 19 16 and -5

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Q: 6. Determine if {(x, y): x^2 + y^2 ≥ 8} is a subspace of R^2

A: The given set is {(x, y) | x2 + y2 ≥ 8}. We check whether the set is a subspace of R2.  Since the…

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = - C 12 = 0 2 0

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Q: u1 O Given a subset U of R² defined by U = |2u1 = u2 Show that U is U2 a subspace of R3

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

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Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: Find the orthogonal projection of 0 0 -9 0 onto the subspace V of Rª spanned by -1 -1 -1 proj, (v) =…

A: Let V be the vector space spanned by v1,v2,v3,.....vn. The projection of v onto V is obtained as,…

Q: 10 Find the projection of 69 -15 -4 subspace W of R³ spanned by -6 and - 14 onto the √] 6 -

A: Given v→=10-14-15 The objective is to find the projW(v→).

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = TT +-18]

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

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Q: -(80) (b) 2. The subspace (a) x+y+z= By in R³ is a plane whose equation is x-2=0 (c) y x-2y+z=0 (d)…

A: Here i am using linear combination and then we saw the relation between the coordinates.

Q: Let S € R² | xy ≥ 0 Y where S uses the usual definitions for vector addition and scalar…

A: Given subset of is the following :Obviously Here noted that vector addition rule : and scalar…

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = --B 7 010

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (7) 0 -8 v= 0 0·00 ||

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Q: Find the limit. Enter DNE if the limit does not exist. lim (2,y) + (0,0) x² + 14y2

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw(7) = = -15] -8 v = -16…

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = 16 -20 -6 = 16 9…

A: We have to find the orthogonal projection of onto the subspace W of R4 spanned by Let v1 = and v2 =…

Q: If W is a subspace of R" and ax is in W, where a is a nonzero scalar and x is in R". Then x is in W/…

A: We have to check

Q: Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.

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Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: 1

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