Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such that V1 V1 = 38, v2 V2 = 162, v3 - V3 = 36, w. v₁ = 114, w v2 = -324, w v3 = -108, then w= VI+ V2+ V3.

Q: Consider A = ⟨0, 4, 2⟩, B = ⟨6, −1, 0⟩ and C = ⟨3, 0, 1⟩. draw the vectors A, B, and C in…

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Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

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Q: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

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Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: Let J = 31 +43 - K and ✓ = 2₁ +3₁-2k be of two vectors. Find the component and projection U in the…

A: u→=3i+4j-k,v→=2i+3j-2k

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V1, V2, V3) such…

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Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: The objective of the question is to verify if the vector w is equal to the sum of the vectors V1,…

Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

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Q: Determine whether the vectors v₁ =(4,-8, 12), and v₂ = (-5, 10, 15) are linearly independent; if…

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: Let u= and v=. Give two vectors that are perpendicular to both u and v.

A: Consider the vectors

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Given three vectors which span w.

Q: Determine if the vectors are linearly independent or not

A: The vectors are linearly independent.

Q: 12 2 14- = -3 are 3 Determine if the pair of vectors V₁ = 3₂ orthogonal.

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Q: Suppose that v1 = (5, 2, 0, 3), v2 = (2, -2, 8, 2) and v3 = (-6, 0, 5, 4). Is the following vector…

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Q: Suppose that v1 = (5, 1, 0, 5), v2 = (5, -3, 6, 2) and v3 = (-5,0, 5, 2). %3! Is the following…

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Q: 3.- Define the vector that allows the linear combination and if it exists, demonstrate the linear…

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Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: 4. (a) Determine if the four points P¿(1,1, –2), P2(4, 0, –3), P3(1,–5,10), and P,(-7,2, 4) lie on…

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Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: lowing vector in the span{V₁, V₂, V3}? 8,9) me vector is in the span. me vector is not in the span.

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Q: Suppose that v1 = (4, 1, 0, 4), v2 = (2, -4, 5, 2) and v3 = (-2, 0, 3, 6). Is the following vector…

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

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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