Assume that V₁, V₂, and v3 are vectors in R3 that have their initial points at the origin. Determine whether the three vectors lie in a plane. v₁ = (2,-3,0) V₂ = (2,1,6) V₁ = (5,0,-4) Vectors do not lie in a plane. O Vectors lie in a plane.

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Find the value of a so that the vectors a = (34, -22, 49), b= (5, 51, 35). and c = (a, -394, -14)…

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Q: sider the following coordinates and vectors, A(-2, 1, 0), B(2, -2,0), u = 3i + 2k, v = 4i + 7j+5k,…

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Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: Simplify the rational expression. X- 1 1-x

A: We have to simplify

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: List five vectors in Span{V₁, V₂}. Do not make a sketch. 6 40-0 V₁ = 3. V₂ = 3 8 6 List five vectors…

A: The given vectors v1=63-8, v2=-630. We have to find five vectors in the Spanv1, v2.