For each of the following sets, if possible, write the set as null(A) or im(A) for some matrix A. Otherwise, show that it is not a subspace. T 2r+t *U-{(1) MATER) {(₁ a) = : r, s, tER s-r-t -6t b) V = {(x, y, z, w) ≤ R¹ : x+y=z+w and 3z - x = 2 = 2yw} c) The plane in R3 containing the points (1. 1. 1). (1.2.-1), and (0.-1.1).

Q: If V3(R) is a vector space and W₁ = {(a,0, c): a, c = R} and W₂ = {(0,b,c): b, c = R} are two…

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Q: Is the set of all vectors (x, y) in R, with the usual addition and scalar multiplication, a subspace…

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Q: Let v₁ = (2,1,0,−1), v2 = (0, 1, 2, 1), and b = (1, 8, –1, −7). Let W be the subspace or R4 spanned…

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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: Let L = {(2, −1, 6), (2, −4,3), (4, −13, 1)}. a) Show why I does not generate the full vector space…

A: This answer is given below.Explanation:

Q: 2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial).…

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Q: if W is the subspace spanned for the 3 vectors, find the sets that serve as a basis for W choices:…

A: The given vectors: v1=-1-75  ,    v2=4-59 ,    v3=69-1

Q: . Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) :…

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Q: If scalar multiplication and addition is redefined on R² in the following way, show that it is NOT a…

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Q: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

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Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

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Q: Let Rz, be a linear space with all polynomials p(x)= ar² + bx+c(a,b,c R) whose degree is no more…

A: Note: As per our guidelines, we can answer the first question. Please repost the remaining…

Q: Determine whether or not W = {[a, a?, b] | a and b are real numbers} is a subspace of R³. Justify…

A: See the detailed solution below.

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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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: Show that every subspace of ℝ is either {0} or ℝ.

A: Given: ℝ. To Show: Every subspace of ℝ is either {0} or ℝ.

Q: C: Let A = (v₁,...,04) be any list of 4 vectors in the vector space V. Let B = (v₁-V2, V₁-V3, V1-V4,…

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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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