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: Under what conditions on the sacalr 'a' are the  vectors (a,1,0),(1,a,1) and (0,1,a) in R\power{3}…

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A: See the detailed solution below.

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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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