verify that det(A B) = det(B A) and determine whether the equality det(A + B) = det(A) + det(B) holds."

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: (a) please find the value of A and B  (b) The support of (U,V), namely the values of u and v that…

A: Given,and..To find the value of A, and the support of..

Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

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Q: 4. Let aj = 9. and b = 63 , a2 = 45 (a) Write b as a linear combination of a1 and a2. b = aj + a2.…

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Q: Exercise 1. Suppose t₁ (n) = O(n²) and t₂(n) = O(n²). Encircle in the following list all the…

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Q: For which value of x is A = x = 4 1 -4 4 0 -3 0 1 x NOT invertible?

A: The objective of this question is to find the value of x for which the given matrix A is not…

Q: 1 -1 0 1. Let A=(23¹), B(4). 3 -5 (a) Compute AB and BA. (b) Compute A + B and B + A. (c) If c = 3,…

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Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: -1 2 1 Let A Compute AAT and AT A. 1 0 1 1 -1

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Q: 1. Let Q(v2) = {a+b/2| a, b E Q}. Prove that Q(/2) = Q[x]/(x² – 2).

A: We have to show that isomorphism means there is function ϕ such that we have to show that it is an…

Q: Compute 5f – 7g, given that f(r) - and g(z) - e. -1) "(z-1) Se

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Q: Let a=⟨−3,−2,2⟩ and b=⟨−4,−2,0⟩ Compute:

A: Given that          a = <-3, -2, 2 >    and    b = <-4, -2, 0> Here we have to compute…

Q: Suppose that Pr[A|B]=4/7, Pr[B|A]=8/13, and Pr[A′]=8/21. Find Pr[A∩B′].

A: To calculate the required probability (using the data on conditional probability)

Q: (c) The inverse of p = q is ~q→~p. (d) To prove "V n, p(n)" is true, it takes only one example. (e)…

A: (c) The inverse of p→q is ~q→~p The inverse of p→q is ~p→~q hence the given statement is FALSE   (d)…

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

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Q: Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2,…

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