10 1301 The dimension of N(AL the null space of A = 0 2000 1 is 10141 1 [202602. O a. none of these Ob.3 O.1 O e.4

Q: j. (21 – 3j + k) +3 -1 -3 Evaluate * (2î – †) · (3î + k)

A: Here we need to find the dot product of the given vectors.

Q: v² = 2| A ds

A: Use the definition of velocity and acceleration, to obtain the required equation. The rate of…

Q: Fmid the value of k frs shich the has yoten 2x, + 4223k i Infimite 8luhen Ho

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Q: Which of the following would be a valid post-condition of the following Hoare triple? x = = (i+1)!.…

A:

Q: Let w z. In(zy z"), then which of the following is ZZL O a. 0 Ob.

A: Given a function w in three variables x, y and z as  and we have to find the partial derivative of…

Q: 1. xlnxlnydy tdoo

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Q: en P(x >4|X

A: Given : Probability,p = 0.5 number of trial,n = 7 Let x be the random variable that…

Q: (15) Let A= [1 01 [2 1] and B= [2 01 L-1 1] Compute AB

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Q: 12004 y-5x-2, expressing non-integer values in the form + Vb, where a and b are integers.

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Q: 3.6-3. Let X, X..Xs be trom a chi-square distributic -1 and e 2. (a) How is Y SX distr 18

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Q: Qil classify the following sequncey © {√√√n } Ⓒ [to)" -n²} Ⓒ {²}

A: Given the Sequence: n -1n.n2 n-1n We need to classify the given sequences.

Q: Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

A:

Q: 01 find 22and 22 find 07 for we xtesny, awit,), 2w ) %3D he

A: z=xyx2+y2

Q: If fo) = x + 1 then (/(2r)) at x= 1 O a. 2 O b. 1 Oc8 O d. 4

A: This question is about differentiation of functions

Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: Question Let LRR be a linear map such that (3,0,1) = (2,7,11) and p(1,0,0) = (1,2,4). Then the value…

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

Q: G=(R,+), H=(Z,+), then [G:H] is O 2 O None of them O Infinite O 1

A: We have to solve given problem:

Q: Let v=i-3j+k and w=i+j-k . Then (-3)||v-3w||:

A: Given,          v→=i-3j+k and w→=i+j-k.

Q: 1. Let, a1 = 7 and for n 2, an An-1 express an in terms ofn. %3D ". **

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Q: Given d, = and dy = Then d, and d, are not - conjugateif Non of these O D

A: Given d0 = -11  and  d1 = 56

Q: Let G = R \ {-1}. Define * on G by a * b = a + ab + b. 1. Compute 2-² in G 2. Find the solution of…

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Q: Let gcd(a, b) = d then which of the following is correct (i) (ii) b|d (iii) d|(ax – by) v[p a. All…

A: gcd(a,b) = d  So, by definition, d | a and, d | b  &, d | (ax - by) for all integers x & y…

Q: 29. For any odd integer n, n° n² +3 %3D 4 4

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Q: (2+31) Simplify (7-4i) 16)

A: We have to simplify the following -  (2+3i)(7-4i)

Q: Select the reason that best supports Statement 2 in the given proof. A. Transitive Property B. Given…

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Q: 4. [MO51] Classify the following PDE: a. 2 uxx = Uxy- 4uy a u b. ax2 a u a2 u ne +3 +u 0 +4 ne +. ay…

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Q: a²-a² = [2²2² (2²]. Let A = Then for any a, Select one: det(A) ≥ 0 O A is singular O None of them O…

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Q: 2 Let M 2 8 Find formulas for the entries of M", where n is a positive integer. 1001 100 J M" = 27

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Q: 21 12x + x4 Evaluate 19 dx - 6x2 + 7 x3 – 19x + C, Where C is the parameter 6x² + 7 x³ 19x + C,…

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Q: n (3+ form atbi -64)(12- J-4

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Q: A = 1 - 2 3 k 0 1 2 -k -4

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Q: EXS Find generd soletion for %3D

A: See the attachment

Q: So 20 (x? – 1)ª æ dæ = O 2/5 O 20 O 2 O -2 O -20

A: Definition used -                 Definite integral -                 ∫abf(x)dx =F(b)-F(a)…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.