State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R3 if x = [1,-2,4] and y = [2,4, –2] |

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A: It is false.

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A: Given, If x is an n-vector.

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, 1, −2), v = (1, −3, −2)

A: By Cauchy-Schwarz Inequality for the vectors, we have

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Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {1 +…

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Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩.Express y as the sum of two vectors: one parallel to x, the other…

A: Given that: x=(1,1,1) and y=(0,3, -2) are two  vectors. Let us say,  w = (a, b, c ) is a vector…

Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: If x and y are two n-vectors, then prove that 1 1 (a) x'y< I,l»,- +=1 (Holder incquality) P 9 (b)…

A: Answer :- A) Ans :-

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Q: Show that if u and v are n-vectors, then u · v = uT v.

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Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

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Q: Verify the Cauchy-Schwarz Inequality for the vectors. = (6, 8), v = (5, -2) u = Calculate the…

A: Given : u=6,8v=5,-2

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, −1, 0), v = (0, 1, −1)

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Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

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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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Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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A: The detailed answer and explanation is given below:-

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A: The given vectors are v1=12, v2=34 and v3=56

Q: Verify the triangle inequality for the vectors u and v.u = (1, −1, 0), v = (0, 1, 2)

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

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Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

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Q: Verify the Cauchy-Schwarz Inequality for the vectors. a = (1, 1, -2), b = (1, -3, -2)

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Q: Express the product Ax as a linear combination of the column vectors of A. 1 21 3 + 3 +3 2.

A: The given product, A2×2x2×1=12-3432 Which will result into a vector of order 2×1

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.