(uA)ū and u(Av) as sums of products of the entries

Q: Let n(B) = 5 and n(AUB) = 7. (a) What are the possible values of n(A)? (b) If n(An B) = 0, what are…

A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: P(n) assert n(n+ 1)(2n + 1) j=1 (a) Verify that P(3) is true (b) Express P(k). (c) Express P(k + 1).

A: Consider the provided question, (a) We have to verify that P(3) is true. Substitute n = 3 in…

Q: e havel (² + ¹) - (2) - (2) = Prove that for all positive integers x and y we xy

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Q: (d) Using the result that Var (3)=0²(XTX)-¹ find Var(30), Var(8₁) and Cov(Bo, 31).

A: Using the formula for the variance of β^, we can calculate the variances and covariances of the…

Q: S (s² + 100) (s − 8) } Evaluate ¹{.

A:

Q: Let A || 9 3 -13 -4 0 0 -5 (a) Find the characteristic polynomial of A. (b) Find the two eigenvalues…

A: In this question, we will find the eigen values and eigen vector.

Q: n n-r+1 (a) Prove that "C, =""C,-1 (b) Prove that "C, r

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Q: (2) Consider for² - 4x dx (a) Estimate this using 4 rectangles using left endpoints. (b) Estimate…

A: The given integral is ∫06x2-4x dx. To Evaluate: the above integral using, (a) Left endpoints using 4…

Q: (a) Prove that rank (AB) <=rank(B). (b) Give an example in which rank(AB) < rank(B)

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Q: (1+v2)+i_ Z2 (1+2) (b) Show that -i 2

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Q: Using the recursive relation I (r + 1) = r[ (r) and the fact that I ย relat 1 2 }} 5 {} and (b) £ =…

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Q: Give the equation of line for this graph; use two decimal places of accuracy. y = x+

A: According to the graph the line passes through two points (164,161) and (179,171). So to find the…

Q: 2 Prove that it a) = (a+b) = (- 1/(-a)= -( - عاها - (a+b) = (- (-a7²b) + (a+b))

A: To prove these properties, you can use the properties of real numbers and basic algebraic…

Q: Consider the function fa : [1,2)R defined by : fa(2) = 6- 2r. The expression of the upper sums,…

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Q: 16 n+ 3 2: Find the remainder when 5 + 2 (14!) is divided by 17.

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Q: Smplify (gizi) (i 131)(5+41)

A: First we will find the multiplication of two factors. Then multiple the result by rest factor. Here…

Q: P(ANB) = P(A)NP(B).

A:

Q: (a) Prove that 1^2+2^2+3^2+………..+n2= n(n+1) (2n+1) divided by 6 For all positive integers n.  (b)…

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Q: Find all positive integers a, b such that a | b^2-b+1 and b | a^2-a+1

A: Solution :-

Q: 6s + 33 Find the inverse Laplace transform of F(s) s2 + 9s + 18 f(t) =

A: We will find out the inverse Laplace transform.

Q: has its largest value. a = Find two numbers a and b with a ≤ b such that b= # # L (6-52 (6-5x-x²)…

A: Given integral is ∫ab6−5x−x213dx. We have to find the value of a and b with a≤b. The integral…

Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: Find the area of the shaded region. f(x) =x - 8x° +21x2, g(x)= 20x+50

A: INTRODUCTION: If the straight line is above the curve in the bounded region, the straight line's…

Q: „¸ 1) and ♂ = (1, 1, 2). Find || ☎ – proj♂¯||. d) 2√3 3 (e) None of these

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Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…

A: We have to show that,  the distinct polynomials x4+x  and x2+x in ℤ3x determine the same function…

Q: In the second order linear ODE with constant coefficients ау +by'+с%3D0 the coefficient a should be…

A: Now we will solve the problem.

Q: if z=x+iy find real x and y such that |z+3|=1-i(z-2)

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Q: expand about z=1 (z+1)(z-2)*

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Q: dx 4x2 -8x + a a. S そ m 14cx-0+51+ s5 tom'/22 4 -2 b. I m1a(x-1)"+51-55 toni" )+c Ciln14 Cx-1)+sl+…

A: