Consider following five sets: 1. { <1, -1>, <1, 1> } { <0, 0> } II. { <1, -1> } III. IV. { <1, -1>, <1, 1>, <2 , 3> } V. { <1, -1>, <-2, 2> } Find all set(s) who is the basis of R2. (a) I (b) I and IV (c) I and II (d) III, IV and V (e) II (f) II

Q: Because [-37-2]] + [-27-5j]= and The [-21-5j] + [-3i-2j] = we can conclude that vector addition is +…

A: The solution is mentioned below.

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Q: (ExC) Let A be an men Matrix and let Vi, Vz,., Vp be vectors in IR". If vi, Vz,., Vp are linearly…

A: Linearly dependent set

Q: 1 2 . Let uj = |0 u2 = 4 and u3 = 1 1 1 -2 (a) Show that {u1,u2, U3} is an orthogonal set.

A: "Since you have asked multiple question, we will solve the first question for you. If you ant any…

Q: (a) (b) Any set of vectors containing the zero vector is linearly dependent. Any set of more than ʼn…

A: Let  be a sub set of  containing the zero vector               Then consider the following…

Q: (1) Show clearly the equation that you need to set up to explicitly test span (try to build the…

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Q: 5. Given the bases B and C, and the given vector in one the bases, find the coordinate vector in the…

A: Please see the below pictures for detailed solution.

Q: b) Then find the projection of b=(3,1,-3,4) onto the column space of 0 1 A 1 1 1 2

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Q: 5. Determine if each set is linearly independent. If the set is linearly dependent, give an example…

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Q: Given the ordered basis B=A₁ -1 0 -[5], 42 - [8 A₂ -2 6 (4]} 8 16 -33 -1 3 [¹].4 A4 0 -9 A3 - find…

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Q: nd a basis for the set of all vectors of the form below, where a, b, c are real numbers. [ a-2b+5c,…

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Q: Q.2) For VR2 and B = {(1,2), (3, 4)"}, C = {(7,3), (4,2)"}; consider one vector v = = (1,0) ¹. •…

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Q: Determines whether or not the given set of vectors is a basis for the R² space. justify your answer…

A: A Given set of vector is −4,4,4,8. We have to determine whether or not the given set of vectors is a…

Q: Find the representation of (9, -2, -3) in each of the following ordered bases. Your answers should…

A: Handwritten solution provided.Explanation:Step 1:Step 2:

Q: 2) Let S contain vectors of the form Then a basis for S would be: a b : a-5b-6c = 0 and…

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Q: a + b+c a + 26 + 4c + 2d` 3. Let m(a, b, c, d) = and set (а+ 2b + 3с + d a+ 2b+ 3c+ 2d) {m(a, b, c,…

A: We have to determine the dimension of the subspace M of M2(R) .

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.