Let U = span{u₁, U₂}and W = span{w₁, W₂} be subspaces of R³ such that 1 2 0,4₂ = 1 1 3 Fina a vector x E UNW such that x = 0 U₁ = and 2 1 W₁ = 0, W₂ = 1 0 -2

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A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

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Q: Problem 6. Let U = {(x, y, x+2y, 2x − y,x+y) | x, y € F}. Find a subspace V of F³ such that F5 = UV.

A: Recall direct sum is sum but intersection is trivial space {0}.

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Q: 2. Let x be a real number. Prove that for every e > 0 there exist two rational numbers q and q' such…

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Q: 7. 555679.32 8. (3.6) 5

A: We convert the whole number and fractional parts separately and then combine the results.

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A: We have to apply the partial differentiation to find solution of the given problem.

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Q: Determine whether or not the following matrices have a Cholesky factorization; if they Ho, compute…

A: Given : A=1-20-2136065      ,     B=4-40-440005 To Find : Cholesky factorization of given matrices .

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Q: The sequence s : 1, 1, 3, 5, 6, 7, 3, 2, 5, 5, 5, 4, 0, 2, 8, 11, 13, 1, 5 is graphical.

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