.. Let X, Y, Z be random variables each having a mean µ and variance o². rurther, let Cov(X, Y) = 2, Cov(X, Z) = 3 and Cov(Y, Z) = 1. Define U = 2X – Y + 3Z.

Q: For what values of z and y is orthogonal to both (-1 and

A: Remark: We know that two vectors are orthogonal if they are perpendicular to each other. i.e., the…

Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

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Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: 1. Find the value for a and the value for b such that au + bv = w if u=(-2,3), v= (1,–3), and…

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Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

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Q: (first three digits), v = 1 4 (last four digits) 6. Let u = %3D %3D 5 2 15 7 4 9 Let A = (place your…

A: 1. We are given two vectors, u→=0215, v→=7491 .We have to find the projection of v→ onto u→, whose…

Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: Which of the following sets is linearly independent? M={ (1,1,3),(3, 2, 0), ( 4 , 5 , 6 )} O…

A: x,y,z  are linearly independent if for linear combination ax+by+cz=0, have unique solution, that is…

Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: -0-0-0-0 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the…

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: 1 1 Let A = Find the values of a such that A is not diagonalizable 1 1 0 0 1

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Q: Let u = and v = . Now, w = is a linear combination of i and v. That is, w = aju + azv. Determine…

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Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: If A is diagonalizable, then A is similar to D. Select one: O True O False

A: Given   if matrix a is diagonalizable then A is SIMILAR  to D

Q: Let A = {1, 2, 3} and B = {1, 3, 5}. Let A × B denote the Cartesian product of A and B. Indicate if…

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Q: Compute u – 3v, u v and u x w.

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Q: Let u = , v = and w = . Now, i = is a linear combination of ü, v and w. That is, i = aju + azv +…

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Q: For what value of h is the following set linearly dependent? S = {2x +2, 2x² + 4x - 7, 2x² - 10x +…

A: According to the given data, find the value of h:

Q: If u = 2i + 5j; v = i - 2j; w = 3i - j, so u + v * w is:   -3   3   6 -6  9

A: Given that: u = 2i + 5jv = i - 2jw = 3i - j To find: u + vw

Q: For which values of C is the set C linearly dependent? 3. C = -1, 2 C=-1,-2 C=1,-2 C= - 1, 1 O c=1,…

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Q: a. Is S = {v1, V2, V3} linearly independent

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Q: Let $(u, v) = (u², v). Find the following images under (a) The u-axis O the positive x-axis…

A: Given, Part a)  i) To find the image of u-axis under Since the v coordinate of points on u axis is…

Q: Show that the set S= {(20, 34), (40, 68)} is linearly independent or not?

A: Given set is S= {(20, 34), (40, 68)}

Q: Determine whether b can be written as a linear combination of a, and a2. In other words, determine…

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Q: Compute u X v.

A: Here given vector u=-123, v=2-4-6 Now it can be written as u=-i+2j+3kv=2i-4j-6j Thus vector uXv is…

Q: Determine whether b can be written as a linear combination of a₁, a₂, and a3. In other words,…

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Q: Is i,,3 a linearly independent set?d O Given ū;| and Ĵs 2 2. 2. -3 3

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Q: How is w = (-3, –13, 7) e R³ a linear combination of (0, -2, 2) and (1, 3, –1)? U = | V = O A. w =…

A: Given query is to find the correct option for linear combination.