Prove the Triangle Inequality |v+w| <= |v| + |w|  (Hint: Use Cauchy Schwartz)

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Q: Prove the Cauchy-Schwarz Inequality, ∣u ∙ v∣ ≤ ∣ u∣∣  ∣ v ∣∣.

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Q: 3. Using the triangle inequality, show that |d(x, z)– d(y, z)|S d(x, y).

A: Its the simply a corollary of triangle inequality

Q: Consider the set = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X Show that x₁ + x2 + x3 ≤ 2 is…

A: Here, in the question a set is given : X={x∈R4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4 ∈ {0, 1} } We…

Q: 1) @ê Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X3, X4 = {0, 1}}. Show…

A: Given: Set: X=x∈ℝ4 / 93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1To Show: b) ConvX is a…

Q: 2 -·---·--· , = 3 II. Let v₁ = Is w in span{v1, V2, V3}? = 2 and w= 1 2

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Q: a) ||x|| = (x1)² + (x2)² (Euclidian norm) b) ||x|| = (x1)² + 5(x2)² c) ||x|| = |x4| + |x2|

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Q: (a) Let a, b e V and suppose that ||b+a|| = 0 and ||b – a|| = 0. What can be said about a, b? Prove…

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Q: Let u = and v =| [:]} Use the Cauchy-Schwarz inequality to show that a² + b? 2 + (*) a +b 2 VI

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A: This is a problem of differential geometry.

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Q: V = {ax² + bx +3|a, b ≤ R} ≤ P₂.

A: The main objective is to show that V is not span of P2.

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Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

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