If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:      W\index{1}={(x,y,0):x,y∈R}      W\index{2}={(0,y,z):y,z∈R}  then V is not the direct sum of W\index{1} and W\index{2}.

Q: How many paths are there from the point (0, 0) to the point (4, 5) in the plane such that each step…

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Q: Find the Jacobian a(x, y, z) a(u, v, w) for the indicated change of variables. If x = f(u, v, w), y…

A: x=ρ sinφ cosθy=ρ sinφ sinθz=ρ cosφ

Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

A: See the detailed solution below.

Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Find the volume of the parallelepiped defined by the vectors u=(1,-8,2), v=(5,0,-3), w = (1,5,-3)

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Q: let B={(1,1,1),(1,1,0),(1,0,0))} base of IR^3 be the coordinate vector of v=(2,3,-2), with respect…

A: Given basis of  isWe have to find the coordinate vector of  with respect to the basis B.We know that

Q: Explain why each set of information does not define a unique plane in three-space. a) x-intercept…

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Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

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Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Find the volume of the parallelepiped defined by the vectors u=(1,-8,2), v=(5,0,-3), w = (1,5,-3)

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Q: what is the sum of a+b+c of the intersection of the plane and line parameterized by x=r, y=1+r,…

A: A plane perpendicular to a vector and through a point In vector form, a plane's equation is…