Have the vector space R³ given with the inner product <> : := 4a₁b₁ + 3a₂b2 + a3b3 With u =<4 2 -1¹, use the indicated inner product in answering. 1. Find a basis B for {u}+ 2. Transform that basis B to an orthogonal basis B₁. 3. Find an orthogonal basis B, for B3 that contains the set Bo from 2. [αι [b₁ x=a₂ and y=b₂ € R³ La 3. Lb3-

Q: 4. If the following vector field is irrotational (i.e. zero curl), А 3 (аху + Bz3)а, + (3x? — 62)а,…

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Q: 4 b= -3 -8 Calculate the magnitude of the following, giving your answers to 1 d.p. a a+b b 2a -b d…

A: The vectors a=4-3,b=-57, and c=-1-8. We have to calculate the magnitude of the following a. a+bb.…

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Q: Evaluate: if vector OA = (2,3) and OB (-1,-2) Show all steps please

A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

Q: Determine a basis and the dimension of the following subspace of R4. V = span((1, – 1,2, 4)", (1, 1,…

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Q: Find the vector x determined by the given coordinate vector (xlg and the given basis 8.

A: In this question, we have given the Basis set of vector space and the coordinate vector [X]B. By…

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Q: Find a + b, 2a + 3b, |a|, and |a – b|. - а 3 (4, - 3), ь - (-4, 3) a + b = 2а + 3b %3

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Q: Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for…

A: First, we need to write the system of linear equations in augmented matrix form.Then, using row…

Q: Let -4 -1 7 -11 3 -1 A 13 -1 1 -3 13 -1 1 -3 Find orthonormal bases of the kernel and image of A.…

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Q: v = (9,5,6) w = (-8,4,-7) = J

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Q: 1. a) Given the lines L₁ : 7 = (1,2,−4) + t(k+ 1,3k + 1, k − 3) and L₂: x=2-3s, y = 1-10s, z = 3-5s,…

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Q: In Questions 1 and 2, describe each translation using a column vector. 1 c CĎ h CẢ d DE i DB e EA i…

A: Since this is a multipart questions, only 1st question and its first three sub-parts is to be solved…

Q: Let W be the subspace of R4 spanned by the following vectors: 8.) Find a basis for W and state its…

A: Let W be the subspace of ℝ4 spanned by the following vectors: w→1=11-22, w→2=-3103, w→3=51-47,…

Q: Let A = {a1, a2, a3} be an ordered basis for the real vector space V. %3D (a) Find the coordinate…

A: Since you have asked a question with multiple subparts, we will solve the first question for you. If…

Q: 1. Find the equation of the vector from SCS points P;(5, 45°, 30°) to P2(7,120°, 150°). Express your…

A: Given - P1(5,45°,30°) , P2(7,120°,150°) To find - The equation of the vector from P1  to P2 and…

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Q: 2 A = [3 1 12 {].

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Q: V= 12 a. u= NOTE: The span of a finite number of vectors is the set of all finear combinations of t

A: We know that given vector "U" is Linear combination of V1, V2, V3   if U=xV1+ yV2+ zV3…

Q: Suppose that B =(2, 2, 1) and makes 30° with A and A•B = 6.What is the magnitude of A? What is the…

A: We will find out the required values.