В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

Q: 2- - Calculate the part a) using the given countour and assuming that R → o. For part b), use…

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Q: 27 Find (all) the value(s) of c such that ) 3c²n 8. %3D - n=0 (A) c= 3 (В) с 3 4 (C) c = - (D) c = }…

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Q: Let j=8 k=3 let A (0, 7-k), B(6, -k+5). Find all points P on the line y = 9-k such that AP I BP.

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Q: In ADEF, K is the centroid. If KJ=22 find EJ. E G H K D F J

A: Centroid of a triangle devides the each median into 2:1 ratio.

Q: Which of the following is homogenous of smallest degree? (A x+y B) In x - In y x4+y4 x-y D Vx-y

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Q: 4. y=e2 y=e", x= In 2, and x = In 8 %3D

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Q: The projection of onto the line through zero and is a. (G) b. d. 0.

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Q: (a) Show that: (i) dim R" = n (ii) dim R2×2 (iii) dim Pn = n+1 = 4

A: Basis of a vector space: Let us consider a set S⊂V(F) is said to be basis of vector space V over…

Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

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Q: 2) Determine the dimension of Null A and Col A for the marix 1 2 30 0] A =0 0 1 0 1 0 0 0 1 0

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Q: Which of the following is a homogenous of smallest degree? (A) Vx+y В) Inx - Iny x4+y4 x-y D x-y

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Q: Let z = 8x2 + 7y2, and suppose that (x, y) changes from (2, -1) to (2.01, -0.98). (a) Compute Az. Az…

A: We have to find   dz and delta z and compare the the values.

Q: Find a given that ||a i+ (a – 1)j + (a + 1)k|| = 7.

A: Given:

Q: K. 4 12 12 8. 7. Which additional piece of information would prove that A/JK-ALMN? C. NM=15 D. LM=10…

A: The objective is to find out the correct additional piece of information.

Q: f A is a 2 x 2 with det(A) = 5, then det(4A-1) = %3D 80 -) 20 16 5

A: We have to choose the correct answer from the options according to the given condition

Q: a. Let û; be the residuals in the lease square fit of Y; against X; (i = 1,2, ... ,n) and a…

A: Given: We have μi^ as the residual in the least square fit of Yi against Xi(i=1,2,...,n) and a…

Q: Find a number in [0, 1] such that the difference of one third the number from its cube is minimized.…

A: Let the number be x. Let f(x)= x³-x/3 So, f'(x)= 3x²-1/3

Q: If H(r) = 1- 3.r – 3.r2 +6.x is the Hermite interpolation for %3D 0 1 the data in the table f(r) b1…

A: To perform Hermite interpolation with the given data.

Q: a) f a²+ a ECCR) for all a E R, then Poove thot R is Commutalve.

A: According to the company's guideline, we shall prove first Que only. For others, kindly post again…

Q: 2. Solve the given SLE using LU-Factorization X, + Xz +Xz = 3 X, - x, + 4x, = 4 2x, +3x, -5х, -D0

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Q: Q#9) find the clamped cubic spline that interpolates the data ( 1,-1), (3,22), ƒ'(1) = 0, ƒ'(3) = 24

A: Given data is 1,−1, 3,22, f'1=0 and f'3=24. We have to find the clamped cubic spline the…

Q: a) Give a condition on two variables X and Y such that E[XY] = E[X]E[Y]. %3D Suppose that X…

A: Given,a) Let, M be random variable which is independent   of X and Y such that , E(M) = 0    Now,…

Q: 2. Find y' (a) by applying the Product Rule (b) by multiplying the factors to produce a sum of sim…

A: In this question, the concept of derivatives is applied. Derivatives We can use a derivative to…

Q: The generating function of a_{n+1}=8a_{n}+4*, where a,=3 is Ο a. Σ2x)^+Σ (4x) ^Κ O b.…

A: Given an+1=8an+4n+1 Multiply the recurrence relation by xn an+1xn=8anxn+4n+1xn…

Q: In AEFG, L is the centroid. If LJ=9 find EL. H J E K

A: We have given a triangle. In which LJ is the centroid. And we have to find EL

Q: Find an equatlon Of the ine Through G1,2); Perpendicular to me 2x+ 5yt 8=0 line

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Q: 3. Consider the following figure. 2h +1 3h - 6 k M B S Part A: Determine the value of h.

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Q: The base of a three-dimensional figure is bound by the graph y = sin(x) + 1. Vertical cross sections…

A: Let a be the length of each side of a square. Then, the area of the square can be calculate by using…

Q: -1 6 1. Let A= - 3 4 14 4 Fund a) M, and Cl b) Mu3 and C43 c) Fund detA by a Cefactor ex panesion…

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Q: Determine the order and the degree: (y")^3+4(yy^' )^2-xy=0 O A. Order – 3; Degree – 1 B. Order – 1;…

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Q: 2. Let G = Z,xZ4, and find [G:H] for: a) H = {0}xZ4. %3D

A: We have to find [G:H]

Q: 3. Consider the following figure. D. 2h +1 3h-6 k Part A: Determine the value of A.

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Q: Find the gene ral solution of the following DESI XY +y² - x? y' = o %3D

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Q: Using your software, compute BT B and B BT forDiscuss the nature of the results.

A: Given matrix is  B=11213141516 Transpose of the above matrix is given by, BT=11213141516

Q: -2) Calculate A-1 by 2 Let A = 1 2 1 -1 -1 A-' = ÷(-A² + 3A +I). and verify your result by showing…

A: Given: A=12-2121-1-10 Therefore,…

Q: Find the value of k so that the value of S,"(2y – 1) dy is 10. 1 2 3 4

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Q: Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) Show that there must…

A: Cubic intepolation: Given the points  for  of the function , which makes  points and  intervals…

Q: 4. Let R = {m + n/2 | m, n e Z}. (a) Show that m + n/2 is a unit in R if and only if m² – 2n2 =±1.…

A: Its purely algebraic problem.  I have solved algebraically

Q: A tank contalne 100ky of dub! and 2000 L l water Pu ro wooder entert a tank at He rote 10L/ma The…

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Q: of operathónS. ion using the variable replacements. 2. a'+2b (if a = 4 and b= 5) a=4 b=5

A: Given a = 4 ane b is= 5

Q: 3. If ADEF is dilated by a factor of 7 with a center at point C to produce AD'E'F', which of the…

A: We have to check

Q: 4- Find e' in the form x+iy if z equals a) 2+ 1/2n i b) 0.5 -1.2i

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Q: Write a in the form of a = a„T+a„N at t = 0 without finding T and N first if r(1)=(2+3¢+ 3¢°)i+(4+…

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Q: Find all values of A for which det(A) = 0, using the method of this section. %3D a – 7 0 A = 6 1– 1

A: Given matrix is A=λ-7000λ506λ-1. Also given that det (A) =0…

Q: 27 Find (all) the value(s) of c such that 3cn %3D - 8. n=0 (A) c= 3 (B) c= 4 (C) c = (D) e (E) e (F)…

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Q: 2- Calculate the part a) using the given countour and assuming that R → o. For part b), e 3ix use…

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

Q: This water tank has dimensions as shown, in metres. 1. Show that the volume of the tank, V m3, is…

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Q: Find f, and f and evaluate each at the given point. F(x, y) = e*y?, (In 4, 2) f(x, y) f,(x, y) =…

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