Consider two subspaces U and V of R¹ below, determine bases of U, V, and UnV, write your Gaussian elimination in tableau form. 1 3 U = span[u1 1 2 U2:= -3 u3 := 3 -6 1 1 3 1 3 4 V = span[v1 1 1 2 V2= -4 V3= -3 -7 2 3 5

Q: Let the set {v,, v2} be linearly dependent. Determine whether the set {v, + 4v,, 5v, - v2} is also…

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Q: and Consider the subspaces -3 of V = R¹X3. Find a matrix X € V such that Un W = span{X}. x=[ -12 (O…

A: Consider the subspaces  and  of .Find a matrix  such that .

Q: The vector x is in a subspace H with a basis B = {b₁,b2}. Find the B-coordinate vector of x. 1 -2 -6…

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Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: Either use an appropriate theorem to show that the given set, W, is a vector space, or find a…

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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)

Q: Determine by inspection whether the given set of vectors is linearly dependent of independent. Do…

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Q: Find a basis of the following linear system. { X1 2x1 x1 3x3 4x2 x2 + x3 + 2x2 + + 3x3 + 7x4 7x4…

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Q: Get a base for your null space. Indicates which dimension it is in. The matrix is shown in the…

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Q: Determine whether U is a subspace of R³. U = {(2r, –s²,t)lr,s, and t E R}

A: Vector Subspace Test: A non-empty subset W of a vector space V is a vector subspace of V if and only…

Q: Consider the linear map T : Rª →→→ R¹, x→→→→ Ax, where [0 2 0 1 2 1 For which a is T one-to-one? A…

A: The given matrix,The aim is to find the values of  for which the linear map  is one-to-one.

Q: Find a basis of the following subspace of R³: W linear independence. {(a+b,b+c, c-a)}. Hint:…

A: Given Subspace is, W={(a+b,b+c,c-a):a,b,c∈ℝ}   Now, (a+b,b+c,c-a) =a(1,0,-1)+b(1,1,0)+c(0,1,1)   So,…

Q: 5.6. Are the polynomials 1-2x+3x², 2+x-x², 1-2x+x² linearly independent in the vector space P₂? If…

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Q: Find the dimension of the subspace spanned by the given vectors.

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Q: If V is a subspace of M5x5 (R) such that dim(V) = 2, what is dim(V+)? 07 10 3 23

A: Given that  is a subspace of  such that .The aim is to find .

Q: Section B: Determine of the following set W is subspace of V=R³: W-{(a, 1, 1): a ER).

A: We have to determine whether the set W is a subspace of V=R3.…

Q: Find a basis for the subspace spanned by the given vectors. 3 Span 3 -1,2 1 3 4

A: The given subspace consist of all vectors in Span-231, 3-12, 123, -154. Take S=-231, 3-12, 123,…

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} O S is linearly dependent. O…

A: Consider the given functions. S=1-x,1-x2,-1-4x+5x2 Let S is linearly independent and there exist…

Q: 5. Let U = {(u1, U2, U3) E R3³|u₁ + u2u3 = 0} and V = {(v₁, V2, V3) E R³|v1 - 302 +503 = 0}. (a)…

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Q: x1 x2 Let W be the subset of R4 consisting of all vectors such that 1-2x2 = 4x3 and 2x1 = x3 + 3x4.…

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Q: Find the orthogonal decomposition of v with respect to the subspace W. (That is, write v as w+u with…

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Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

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Q: Which of the following vectors are linearly independent? I know that you can use row operation to…

A: To determine if a set of vectors is linearly independent, use the following techniques:1. Zero…