Determine if set S is a subspace or not S = {(a,0₁0) € R² } Ⓒ @ 3 S = {(₁₁ 6₂c) | b=a+c} in R (3) S = { (₁₁ b, c) | b = a + c + (a, 1} in R³

Q: Which of the following is the dimension of the subspace b W = :a = b - c and a, b, c,d eRC R* ? (a)…

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Q: Answer the following: A SIAII OT VOITOUG 4. Determine if the odd functions (f(-x) = -f(x)) are a…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: Which one of the following is a subspace of P3 (A) The set of all polynomials of degree 1 (B) {a +…

A: Given a vector space V, let W be subset of V , then W is called subspace of V iff If u and v are…

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

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Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: 2. Determine whether or not the following subsets of the given vector spaces, are subspaces: (a) The…

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Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 2 - 1 y= a. 3/6 -2/6 丽··· -1/6…

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Q: Q: Let W, ={(a, B.Y, 8): a=y+28, y= 28} and W2 {(a, B.Y, 8):a-y-0} be two subspaces of V,(R). Find a…

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Q: Determine whether S={a, +a,x+a,x :a, +a, +a, = 0} is a subspace of P.

A: Here S is a subspace of P2

Q: Let V₁ 1 -2 3 2 {V1, V2,V3}. V₂ = 2 -2 V3 7 8 7 - 10 and u = Is u in the subspace of R4 generated by…

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Q: I) Show that W = {(a, b,a-b): a, b e R) is a subspace of R³ and find its dimension.

A: W = {(a, b, a - b) : a, b ∈ R} Clearly, W is a subset of R3.     Let, (a1, b1, a1 - b1), (a2, b2, a2…

Q: Find the orthogonal projection of the vector [ 49 49 49] onto the subspaces of R3 spanned by [2 3…

A: We have to find the orthogonal projection of the vector  onto the subspace of  spanned by  and .

Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

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Q: Verify whether the following sets are subspace of R³/R¹ or not. (i) S = {(x, 2y, 5) : x,y € R} (ii)…

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Q: Q2. Let V = {(a, b, c, d) : b + 2c + d = 0} and W = {(a,b, c, d) : a + 2b = 0, c = 5d} be two…

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Q: 1. Let "W" be the set of vectors of the form below. Show that "W" is a subspace of R4. You must show…

A: To show whether W is the subspace or not.

Q: Show that the set of vectors {(−4, 1, 3), (5, 1, 6), (6, 0, 2)} does not span R3, but that it does…

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Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: The given subspaces of ℝ4 are U1={a, b, c, d) ℝ4| 1b=с; a=d=0};   U2={(a, b, c, d)  ℝ4| a - b + 2c +…

Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: 8. Let W denote the subspace of R5 consisting of all the vectors having coordinates that sum to…

A: Consider the provided question,Write the given vectors into a matrix as below,

Q: Given that V1 = 5 3 V2 = 2 } V3 = 3 7 " 11 10 For what value(s) of h will y be in the subspace of H…

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Q: 1. a. b. x1 + x2 x1 2x1 - X2 Find the solution set of the following system of linear equations : - -…

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Q: Suppose that X = eR' : 2 + y + z = 0 and r²+y² = z² } . Determine (with justification) whether X is…

A: We have to check whether the set X is a subspace of the vector space ℝ3. We have to give a…

Q: Let W be the subspace of Rª defines as X1 X2 W = {x = ER : : x1 – 3x2 + 4x3 – x4}. %3D x3 X4…

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Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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Q: Which of the following sets are subspaces of R3: W1 = {(x1, x2, x3): x3 = 2x1 – 4.x2}; W2 = {(x1,…

A: A set W, is a subspace of a vector space ℝn if it satisfies the following three properties.  0 is…

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: |412 = -a}, verify that S'is a 7. Let S subspace.

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Q: 2

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Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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