Let B={b₁,b₂), and C={C₁,C₂} be Bases for a vector space V, andsuppose b₁ = 4c₁-6c₂, and b₂ = -8c₁+30₂. Given x = 6b₁-4b₂, find [x]c Enter your answer in the form (a,b) with no spaces

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Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: The set ((x,y) : × 20, y 20) with the standard operations in R in not a vector space.

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Q: (c) Show that if a span{b₁,b2, ..., b;} then bib{T bi bi (0.0.3) Hint: You can prove the…

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Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

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Q: Consider two bases B= (b, b2) and C= (c, c2) for a vector space V such that b, =e, - 6cz and by =…

A: Given two bases  and  for a vector space V such that and . Also, given that and we have to find .…

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Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: . u. ): Is the set S = {r +x-1,22 - r+3,-a+3z-2}) a base for the Pa(r) vector space which is a…

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Q: . Let V be a vector space, and {v1, ··· , vn} be a set of vectors that spans V . Show that the set…

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Q: let A = [1 5 -4 -3 0] and w = [1]            [0 1 -2  1  0]              [2]            [0 0  0   0…

A: Answer is in below steps.

Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

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Q: }] respectively. Let y = and u = . Write y as the sum of two orthogonal vectors, y, in the span of…

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Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: Determine a basis for the vector space spanned by the vectors 3. V1 2 ,V2 .Vs 17 12 O A. {V1, V3,…

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Q: (iii) If u = 461 + 362 and [u]c = then the value of r is and the value of S is (iv) If V = 3c1 + 2c2…

A: Given that  b1 = 10c1 +3c2,  b2 =27c1 +8c2 c1 =-8b1 +3b2,   c2=27b1 -10b2

Q: sider the ordered bases B= ((4, –9), (–3,7)) and C = ((4,3), (–2,4)) for the vector space R’ %3D

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Q: Let H = span {V₁, V2, V3, V4}. For each of the following sets of vectors determine whether H is a…

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Q: : Let V be the set of all ordered pairs of real numbers (u1, u). Consider the following addition and…

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A: The main objective is write two non zero vectors in ℝ5. Find the given values.

Q: Given the set R² with the vector addition operation defined by (x₁₂1₁) (x₂, 1/₂) = (x₂+x₂₂3₁ +3₂ −2)…

A: Given a vector addition operation, we want to find the zero vector for the set .

Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

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Q: Determine the scalar triple product u (v x w) of the vectors u = i + 2j + 3k; v= -i-j+k; w = i+j+k…

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Q: Let V1 MECANIS 3 1 11 V2 = 1 0 V3 = SCAMENTO 0

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Q: Consider the following vectors: 2 -3 u = 2 v = w = -6 3 a. Do these vectors form an orthogonal set?…

A: For linearly independent vector set orthogonal is equal to orthonormal vector. Please find the…

Q: Find a vector v such that ||v||=5, and v is in the opposite direction of -5i+7j .

A: We have a vector -5i+7j Let u→=-5i+7j First, we find a unit vector in the direction of u→=-5i+7j The…