Consider the following subspaces U, V, W CR³: U = {(x, y, z): x+y=3z=0} V = {(0, c, 0): e ER} W = {(x, y, z): x + 2y = 0). (a) Show that R³ = U@V. (b) Show that R³U+W, but R³ is not the direct sum of U and W.

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Q: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D

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Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

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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: (b) For subspaces X and Y, the sum X + Y is a direct sum (denoted X + Y) if every VEX + Y can be…

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Q: Determine whether the given set S is a subspace of the vector space V. DA. V = C5 (I), and S is the…

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Q: 2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s…

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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: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

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Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

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

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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: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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Q: Find the closest point to y in the subspace W spanned by U₁ and 02. 2 2, U2 23 13) y = 13 9 41 =

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Q: ) Consider C with the usual inner product, given by (u, v) = ₁₁ + The vectors are orthogonal. Let…

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Q: What is the dimension of the subspace U = -{(8 3 2 6 a b-b C 0 C c): a,b,c : a, b, c ER of M2x4 (R)?…

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Q: Find the orthogonal projection of onto the subspace W of Rª spanned by projw() = v= 4 -2 -13] 3 15…

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