Let us define xy(x² – y²) x² + y? f(x, y) = a. Verify that af _ y(xª – y4 + 4x²y?) (x² + y²)² b. Argue by symmetry that we must have af x(x4 – y4 – 4.x²y²) ду (x² + y²)² c. Now consider the function g1 :t+ fæ(0, t). Differentiate this with respect to t to find fæy(0, 0). Similarly, consider the function g2 : s+ fy(s, 0) and use it to find fyæ(0,0). d. Why do your answers to the above question not violate the Clairaut-Schwarz theorem? You may

Q: Let A4x6 and B. B6x4 then the sıze of AB = Select one: a. 4 x 6 b. 6x4 O C. 6x6 d. 4 x 4

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Q: Use the union rule to answer. If n(A) = 6, n(B) = 11 and n(An B) = 5, what is n(A U B)? n(A U B) =

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Q: If AΦB = AB - B find -2Φ3 Select one: a. -3 b. 9 c. -9 d. none of the options

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Q: Find the values for c1, c2, and c3 to make sure that: c1 (10, 25, 1) + c2 (-15, 5, 0) + c3 (5, 0,…

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Q: If a = 4, y = 3, then 3a + 5 = 20 - y Select one: O True O False

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Q: Let A = {1}, B = {2}, and C = {3}. (a) Explain why A x B B x A. (b) Explain why (A x B) × C # A × (B…

A: Cartesian product: The cartesian product of the sets A and B is defined as the set of all the…

Q: If A={3,4,5}   B={a,b,c}. Find B X A.

A: Explanation of the solution is given below...

Q: Find, if possible, (a) AB and (b) BA.

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Q: Ā = ë, + 3ë, – 2ẽ, -B*=? B = 4ẽ, – ë, Ĉ = -3ẽz– 5ẽ,

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Q: Use the union rule to answer. If n(A) = 9, n(B) = 10 and n(A N B) = 3, what is n(A U B)? ... n(A U…

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Q: Prove: If (where b + 0 and d + 0), then C + d d a + b

A: Consider the given information, If ab=cd then show that a+bb=c+dd. First we consider ab=cd.

Q: Find a, b, c, and d, if а b 1 3 d 2.

A: A matrix is an object with certain number of rows and certain number of columns. An entry in a…

Q: ample. A oB indep, How about their are

A: We know : If two events are independent than occurrence of one does not effect the probability of…

Q: Use the union rule to answer. If n(A) = 6, n(B) = 10 and n(A N B) = 4, what is n(A U B)? n(A U B) =

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Q: Cx-3) Gょ2)tG3)

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Q: Find, if possible, (a) AB and (b) BA.

A: We know the order of a matrix is defined as  ---->  m x n where, m = number of rows…

Q: For u=⟨4,−2⟩ and v=⟨−5​,5⟩​,find u•v.

A:

Q: Use the union rule to answer. If n(A) = 10, n(B) = 15 and n(AB) = 8, what is n(A U B)?

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Q: Let A= {2, 4, 6}, B={2, 6}, C={4, 6} and D={4, 6, 8}.

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Q: If a b=2a- 3b+1, what is 3 (-1)? a. 4 b. 10 C. 8 d.-1 b

A: Compare 3*(-1) with a*b, a = 3, b = -1.

Q: The order of (3, 4) in Z4 × Z10 is  a. 4 b. 12 c. 40 d. 5 e. 20

A: The objective is to find the order of 3,4 in Z4×Z10 First find the order of 3 in Z4, then find the…

Q: (B) = 10 and n(A N B) = 4, what is n(A u

A: n(A U B)=12

Q: 1 Determine the values of a, b and c if: 2(a,b,4) +(6,8, c) – 3(7,c,-4) = (-24,3,25)

A: We can solve this as follows:

Q: Let á = (–1, 0, 1), b = (0, 3, − 1) and ₹ = (1, 2, —2). a. Find à x b. b. Find (a + b) x č. c. Find…

A: NOTE: Refresh your page if you can't see any equations. . here we have . find the determinant

Q: If A={1,2} and B={a,b,c}, find: I. A*B II. P(B) III. n(P(A))

A: A={1,2} B={a,b,c} A*B={(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)}     2)P(B)={…

Q: 14 Li=2 =2 XiYi

A: From the provided information,

Q: In the diagram below, if AB= 40, CD = 25, and AD = 80, find BC. D. O 15 O 40 О 25 O 60

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Q: The table shows the movement of a stock for 30 randomly selected trading days. "Up" means the stock…

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Q: if N { A U B }= 90, N {A}= 50, and N{B}= 45, find N {A n B}

A: Given :NAUB=90  NA=50 NB=45

Q: Find AB given that: 2 -4 170 A -35 11 and B- 0 -2 8.

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Q: Find the mode: 76, 25, 76, 13, 25, 29, 56, 76 O a. О а. 47 ОБ. 76 O b. О с. 42.5 O d. 25

A: We have given that,  The data set is,  76, 25, 76, 13, 25, 29, 56, 76 Then,  We will find the mode…

Q: Find the value of a, b, and c if (a+b)(a+b+c)=21, (a+c)(a+b+c)=35, and (b+c)(a+b+c)=42.

A: First we need to make some equations and the we have to simplify them in order to get a, b and c.

Q: 1 -1 2 2 1 -1 A = 2 B = 1 3 2 4 C = 1 -1 4 -4 Find A - B, A+ B, and A + C.

A: Here, A and B are of the same order so A-B and A+B is possible but A+C is not possible because A and…

Q: A хо C 35⁰ B yo С

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Q: 6. (3zy-- 2ay") dx + (x2 - 2axy) dy = 0.

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Q: wherey? ty=25

A:

Q: Find, if possible, (a) AB and (b) BA.

A: Given: two matrix A and B. Find: AB and BA