Q.3 Prove (without expansion) b с d —d с а C -b а = (a² + b? + c² + d²)? -C d а -b -d —с b -C а

Q: d^2B(u)/du^2 ,but where B(u)= 1/(1+u)^7

A: Given B(u)=1(1+u)7To find d2[Bu]du2:

Q: 1. a|b iff ac\bc, where c # 0. 2. If alc and a+ b= c, then a|b. 3. 7|23n – 1, Vn € N -

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Q: ax? +b?y +c°z?) a'x+ b°y+c°z xyz abc X y Z. if - prove that b %3D 3. a

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Q: Given the set of equations M = B² – 3 In B , B = In VN Which of the following is dM/dN? The answer…

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Q: (h) = ? Suppose, a =6a п — 1 - 11a +6a ,+2-3". What is a n - 2 C, 1" + C2 2" + C3 3" С, 1" + C2 n 2"…

A: See the detailed solution below.

Q: a?u a?u a²u 4 ax2 - 2 = 0 дхду ду? n. ди u ду? ax —2 иҳҳ + иxy t 4uyy + 5 их + 5и — 0

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Q: describes. A v 1.4 <r< 5 and 0 <0 < 2n ? v 2.4 <r<5 and a/2 < e< 3n/2 B ? v 3.0 <r<5 and 3/2 < 0< 2n…

A: According to figure shown below, answer all questions.

Q: 6. Johnny knows that AB = XY and BC =E YZ. What other information must he know to rove that AABC =…

A: If there is two triangles then they should be congruent if and only if there corresponding angles…

Q: 3 51 Q2) If A = [, 1 and B = || show that -1 4. (A + B)² # A² + B² + 2AB

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find (a) ∣A∣, (b) ∣B∣, (c) AB, and (d) ∣AB∣. Then verify that ∣A∣∣B∣ = ∣AB∣.

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Q: Let 1 A = - [3 +1], B =[ _4], 0 = [1] -2 3 (a) Show that AB = CB. (b) Can we cancel B from both…

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Q: What is the general solution of (r* + s) dr + s² (3r + ks ) ds = 0 where k is a constat || O 4rs + r…

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Q: v=u+5t make t the subject

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Q: If z, = 1+ jb , Z2 = re¯)² , z1/z2 = -10, determine all possible values of b and r.

A: Consider the provided question,

Q: 6. a. Is A true or false? BAC = True AV ¬(DE)= True (¬B V ¬D) = True b. Is B true or false? A → B AV…

A: 6.a) Hint: If A∨B is true then either A or B is true. If A∧B is true then both A, B are true.

Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

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Q: In the diagram below ABGH, BCFG and CDEF are squares. Prove that 21 + 2 = Z3. A В C D <4 <6 <5. <7…

A: GF/DF =1/√2 FD/FH=√2/2 = 1/√2 So, ∆GFD~ ∆ DFH Angle 1= angle 6

Q: 4- Prove that (a) (b) Ax B|2 = |A|²|B|² - (A.B)² (A x B) (Cx D) = (A C) (BD) - (AD) (B C)

A: Answer is in step 2.

Q: You are given that ||u|| = 1, ||v|| = (би + v) . (и —2v) ? 2 and u • v = -1. What is the value of |

A: Given query is to find the value of indicated vector operation.

Q: Let A = -[-32-3] and B = (a) Find AB, A-1, and B-1. AB= 5-3 2-1 A-1 B-1 = (b) Show that (AB)-1 =…

A: a)AB=2-2-235-32-1AB=2(5)-2(2)2(-3)+2-2(5)+3(2)-2(-3)-3AB=10-4-6+2-10+66-3AB=[6-4-43]A-1=1AAdj(A)A-1=…

Q: 2* (2 – 5) 3 f'(z) dz If ƒ (z) = - By Argument principle Find (z – 1) (z – 2) I:l=4 ƒ (z) - 2 Ti…

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Q: |=5| (t - T)e2Tsin2T.dT 52(s² – 45 + 5), Select one: True False

A: We will check whether the given statement is true or false using convolution theorem.

Q: 16. If (2i + Aj) x (i +j-k) = -Ai + 2j – k then A A -3 В -2 C 244 D 3

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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: [2 1] Q2) Assume A = |1 3 .3 4] 2 4 1 and B = l show that (AB)' = B' A' 13 6 4] [

A: Here, it is given that  A=211334 and B=241364. We need to show that (AB)'=B'A'

Q: Evaluate by Algebraic Substitution: * 5. S/1+vz dz -(1-v5)(3VE – 2) +c b. (1+ v7)(3V7 + 2) + C 5(1 +…

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Q: If z̟ = 1 + jb , z2 = re¬j² , z1/z2 = -10, determine all possible values of b and r.

A: According to the given information, it is required to determine the possible values of b and r.

Q: Determine if the following statement is true or false. Motivate your answer. If Re(z) > Re(w) and…

A: We have to check whether the statements, "If Rez&gt;Rew and Imz&gt;Imw then z&gt;w" Is true or…

Q: Q2: Suppose A = (0,2,4,6,8), B = (1,3,5,7) and C= (2,8,4). Find 1) AUB %3D 2) Ance 3) Bnc 4) C\B

A: Given A = 0 , 2 , 4 , 6 , 8B = {1 , 3 , 5 , 7}C = {2 , 8 , 4} then (1) A∪B = {x : x∈A or x∈B}= {0 ,…

Q: 1- Prove that (a) |A× B|² = |A|2|B|? – (A · B)² (b) (Ax B)(C × D) = (A· C)(B· D) – (A · D)(B · C)…

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Q: 3. Show that a2 + b2 + c2 > ab + bc + ca and using this result show that (a) (a + b + c)2 > 3(ab +…

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Q: Exercise 2.51. Let A, C C X and B, D CY. (1) Show that Ax BC X x Y. (2) Prove or disprove: (X \ A) ×…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: [12 31 1 2 and B = ] 1) If JA| = |B1, find the value of k where A =0 %3D 13 [2 1

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Q: (b) Find An (B U C), (A n B) U c, and (A n B) U (A n C). (Enter your answer in An (B U C) : (A n B)…

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Q: Q3) Assume A = [4 16 3 11 7 21 [3 21 and B = 1 5 (3 14 3 show that (AB)' = B' A'

A: Given, A=431672B=321543

Q: а. 2 ихх — иху — 4uy a2 u az u b. əx² azu ди +4 +34 + u = 0 дхду a?u = 2", k < 0 ax ду ди C. k ax?…

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Q: Find (a) ∣A∣, (b) ∣B∣, (c) AB, and (d) ∣AB∣. Then verify that ∣A∣∣B∣ = ∣AB∣.

A: Given matrix are A=012543768,B=2121-1003-2 (a)…

Q: 2. Ifj || k a. mZ2%3D b. mZ3 = 47° 1 119° %3D k %D C. m/1 = 3.

A: j || k

Q: 2 11 Q2) Assume A = |1 3 [3 2 4 1 and B = show that (AB)' = B' A' %3D 3 6 4J 4]

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Q: 6. a. Is A true or false? BAC = True AV (DE)= True (¬BV ¬D) = True b. Is B true or false? A → B AV…

A: Given Data: Let us consider the given data , a)Is A true or false? b) Is B true or false? c) Is A…

Q: 8. Given that P(x + 2) + Q(x + 1) = x , the values of P and Q respectively are A 1 and -2 B -1 and 2…

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Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: Q3) Assume A = [4 6 3 11 7 2 [32] and B = 1 14 5 show that (AB)' = B' A' 31

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Q: (b): Find the values of V10 (Vab) (1): (a² + b²), (2): and (3): ab(a² + b²) by using fomulas if V5…

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Q: If P(A) = 1 P(B) = 2 and P(A U B) 11 find (i) P(A/B), (ii) P(exactly one of A and B occurs), 12 4…

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Q: 1 2 1 -Given that B= 1 -1 0 3 1 1 Show that B,-B,- 6B = 1. Hence, deduce that B' = B² -- B – 61.

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Q: [2 Q2) Assume A = |1 3 11 show that (AB)' = B' A' 6. 4 and B = 13 4. 213

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Q: Negate the following statements: a. (3y € Q) (y + 4 = 8) b. (Vz E P) (г > 0) Vx3y, M(2x,y) d. 3xVy,…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…