Z1 is complementary to 2; 2 is complementary Given: 2 B 3 A E to 23 Prove: BD || AE

Q: 4-IN THE ADJACENT FIGURE, IF AB = AC AND DB = EC, PROVE THAT ABEC = ACBD

A: Consider the side AB as x. Since AB is equal to AC, so, AC is also equal to x. Consider the side BD…

Q: Q(3): Show that: (a) Vx Vo(r) = 0, and (b) V-VX E(F) = 0.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: : Prove that (→āx5)(cxa) = a.c.a.a 6.c.b.d %3D

A: We use properties of scalar and vector triple product to prove this Question

Q: 6. Let An = [−3⁄, 1 + ¹). Find ♂ Añ and justify (not prove) that your answer is correct. n=1

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Q: Let Give the 2,1 entry of 4-¹. a) 0-¹ b) 0¹/2 c) 03/2 d) 0-5 e) 0-2 f) O None of the above. 02 2 A-1…

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Q: [3 4 11 What is element a22 in B* if B = 2 3 2 lo 1 1]

A: The matrix B is given.  We first find the determinant of B and then adjoint of B and find  B-1…

Q: For which of the following is it true that n(A) + n(B) = n(AUB)? a. A = {a,b,c}, B = {a,b} b. A =…

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Q: A.2 (b) Show that, in general, ßo ‡ Bo, and find in terms of Y;. In what particular case is ßo = Bo?…

A: Simple Linear Regression(SLR)          It is a statistical method that allows us to summarize and…

Q: Let G = (Zj0, X10) then o(G) is а. 5 O b. 4 С. 3 O d. 2 О е. 10

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Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Given: P1: (A V B) ⇒ (CAD) P2: (D V E) ⇒F C: A ⇒ F Prove that P1, P2 - C.

A: Given: P1: A∨B⇒C∧DP2: D∨E⇒FC: A⇒FTo prove: P1, P2├C

Q: :""n e Z*, if n³ = 3k for some k E Z, then n = 3q for some q E Z." %| %3D

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Q: Provide a left-hand-side, right-hand-side proof of the following: dt

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Q: 2 If A= L Rnd O A O A-A"

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Q: If then is equal to Select one: O 10 O none of them O-5 -10 [²f(u)d O-15 f(u)du = 5 and 5 15 […

A: We have to evaluate the integral.

Q: If A = [1 1] then the dimension of N(A) is O a. 1 O b. 3 OcO O d. 2

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: 3 Let A =2E -1 0 B = 0 2 If BXT = A, then X= Select one: -3 0 a. 1 -3 O . 1 -3 O d. None of these 1)

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Q: 7- Evaluate:

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Q: Q4 for all nz 1 we went to Shot that 27

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Q: maximum point of y x²-x-12 X+5

A: Maximum point of y is the point on the graph where y has the larger (maximum) coordinate than any…

Q: 1 2 2 If A 2 2 1 A? – 4A- 51 = Q, =|2 1 2, then prove that

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Q: Suppose A and B If A) = C(B) then a is equal to 2. Or O a a = 4 O b.o 1 Oc 6 Oda = 2

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Q: 25. Find 0 16 18 fB rist to our ai jari 20

A: The angle between two sides is calculated by cosine's rule.

Q: и%3D 19, —8] v = [4, –5] 4u + v = | Ex: 5 :

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Q: ) Find A10 and eAt for [1 1 01 A = 0 0 1. Lo 0 1l

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Q: Let A = {x e Z: 10|x} and let B={xeZ:15|x}. %3D Then * O Bc A O A=B O None of these O ACB

A: Suppose A and B are two sets . Note the following result : If x∈B for all x∈A then A⊆B . If A⊆B and…