C: Let T be the linear operator associated in the standard basis B of F2 with the matrix 2 4 -1 Let B' be the basis ((2, -1), (2, 1)) M = b) Using eachof these three matrices find the dimension of the range of T (you must check that the mension is the same with all the matrices)

Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

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Q: Determine whether the vectors (3,0, 3, 6), (6,0, 0, 3), (0,0,3,0),(6,3,9,12) form a basis of R*.

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Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]);…

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Q: Find the basis for the orthogonal complement V: v1=(1,-3,3,5) v2=(2,-5,9,3)

A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

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Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: 2 COLAS -1 Consider the two bases B= for R² and C= P √2 a.) Compute the change-of-coordinates matrix…

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Determine the dimension of the vector space. M2,3 STEP 1: Determine the number of linearly…

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Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions