18. A vector space V is said to be the direct sum of its subspaces U and W, written V = U®W, if every vector in V can be expressed in exactly one way as v = u+ w, where u is a vector in U and w is a vector in W. a. Prove that V = U@W if and only if every vector in V is the sum of some vector in U and some vector in W and UnW = {0}. %3D b. Let U be the xy-plane and W the z-axis in R'. Is it true that R = U©W? Explain. c. Let U be the xy-plane and W the yz-plane in R'. Can every vector in R' be expressed as the sum of a vector in U and a vector in W? Is it true that R' = UOW? Explain. %3D

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A: Given: 73+45+13 To find: We have to calculate the value.

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A: Solve the (a-5)6

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A: Consider the given expression. y=limx→0+lnxxx Take ln on both sides of the equation.…

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A: Topic = Algebra

Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

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A: NOTE As you don't mention what to find. I am just simplify the expression.

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A: Given :- (a–5)6 Using Formula :- (a–b)3 = a3–b3–3a2b+3ab2

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.