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 = 18, V2 V2 = 99, V3 V3 = 4, . . w V₁ =18, w . * then w = V2 = 693, w V₁+ . V3 = 12, V₂+ V3.

Q: show that the vectors: 2,3), II

A: To prove that the vectors:     v1=(1, 2, 3), v2=(-2, 1, 1), and v3=8, 6, 10 in ℝ3  are linear…

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: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Find vectors u and v whose initial and terminal points are given. Determine whether u and v are…

A: The u vector can be computed as: u=6-1i+11-1ju=5i+10j

Q: Let V₁, V2, V3 be linearly independent vectors in R". Show that {v₁ + V₂, V₂ + V3, V3 + ₁} is also…

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Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

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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: 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: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

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: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

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: What if the vector v was [ 7, 11, 3]

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Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

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: Suppose that v₁ = (4, 4, 0, 7), v₂ = (2, -5, 5, 4) and v3 = (-7, 0, 5, 2). Is the following vector…

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Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

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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: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Determine which vectors that are orthogonal to (– 3, -6)? (-4,2) and (-1,3) (-10, 5) and (-3, 6) a.…

A: To determine the vectors which are orthogonal to -3,-6. (a) Given vectors are -4,2 and -1,3. We know…

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

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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: 5. Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2)…

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