Solve the equation Ax = b by using the LU factorization given for A. 4 - 4 4 1 0 0 4 -4 4 - 4 A = - 12 9 -7 - 3 1 0 0 - 3 5 , b= 27 = 8 - 5 4 2 -1 1 0 1 - 23 Let Ly = b and Ux = y. Solve for x and y. y II

Q: Q2/ Fit a second - order polynomial to the data in the following table: 5 1 4 2 Y 2 3 4 -1 4 6. 6 00

A: Solution

Q: 1) y" – 10y' + 25y = 8e- y(0) = 1, y'(0) = -4;

A: Follow the steps.

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: Exercises: 1) Determine the eigenvalues and the corresponding eigenvectors for the following…

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Q: Q2) Solve the D.E dy – (2x/1– y²)dx = 0

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Q: [a, b, c If Aj = [di e, fi] [a, b2 c2 A2 = [d2 e2 a3 bz c3 Az = [d3 ez f3] and are any 2 x 3…

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Q: Q2) Solve the D.E dy - (2x/1-y2)dx 0

A: The given differential equation is dy - 2x1-y2dx = 0

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: Pianni Beverages produce two ready-mixed cocktail drinks; the Zombie and the Skyjack. Each is a…

A: using the given conditions, let the cocktail ' the Zombie ' be x and the cocktail ' the Skyjack ' be…

Q: a2 b2 C2 If Aj = [di ei fi] A2 = [d2 e2 2] real numbers, show that: 9. (A, +A,) + Az = A, + (A, +A3)

A: # As per the guidelines we are entitled to solve one question at  a time ,please resubmit the other…

Q: Ql: Find the integration of : (, 1. S cos (3 sin x)cos (4 sin x). cosxdx 2. J Tanx sec*x dx 3. 6…

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Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .

Q: If u = x3 + y3 where x = a cos t, y = b sin t, then %3D du dt

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Q: 3+ V9 – 4(3 – i) 21 = 3+ V4i – 3 2 How do you solve for the equation above ?

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Q: √3. (2√27 + √12)

A: Given expression: 3·227+12

Q: Q38: If y = e2* sin 5x, then which of the following is true? e (a) y" – 4y' + 30y = 0+ - (b) y" –…

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Q: [a, b, ci] If A, = [d, e fi] [a2 b, c2] A2 [d2 e2 ] [az bz c3 Az = [d3 ez f3] and are any 2 x 3…

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Q: Given: A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 5, 6}, and C = {1, 6, 7}. Find: B' nC' =

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Q: The set of equivalence classes Zn = {[0], [1], - - · , [n – 1]} is an example of what is ... called…

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Q: dy Find given x' +y =8.y. dx

A: Here we can use implicit differentiation for finding the value of dydx. For the purpose we need to…

Q: Use Newton methad to find fis), f'ca) 9. to 3. 10

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 - y from above inside y = x2 ,y = 4.

A: Volume bounded by xy-plane

Q: Q2/ Fit a second - order polynomial tó thẻ đấtă iñ the folowing ble X 6. 1 2 7 Y 8 3 4 -1 4 6.

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Q: Consider the Solidas bound below by 3= N3(*2+y?), above by 2-1=N= -x?-y2 Its volume V (S); O The…

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Q: If A is 3 x 3 matrix such that (A + I3)² = 0 Show that: A is invertible.

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Q: Consider the solid bounded by the planes: z =x+y, z=12, x=0, y=0. Determine the volume of the solid.…

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Q: [15 6 If F = |7 1 3,G = |4 0 6 [5 4 3 -7 and H = |2 1 7 4 5 1 2 5 6. ,find 2 GH HF

A: We want to find the matrices GH and HF

Q: Q3) Evaluate triple integral , dz dy dx.

A: Q2)

Q: Let the characteristic equation of a 3 X 3 Matrix A be X3 + ad² + 47) – eigenvalue of A is 4 and a…

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Q: Evaluate fa e2z dz, where C is a circle with (z+1)* centre at origin, |z| = 3.

A: Cauchy integral theorem evaluation of the integral.

Q: 2) 3) 12 4) 5) 미. 미이미。 미 미 미 미우 미위미위 미 미 미유 키4 2_3

A: 2. 2540-2440=140

Q: A number is drawn at random from the integers 20 to 40. Let A the event that the number is not less…

A: We have to solve the given problem.

Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 9.

A: Given equation is x2 + y2 + z2 = 9

Q: b) Given f (x)= In x x>0. Use differentiation to find the value of f'(x) at x= 2. Give your answer…

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Q: Q3) Evaluate triple integral S S dz dy dx.

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Q: Solve: (dy/dx) = [(5y - 2x) /(4x – y )] %3D

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Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: There are six P20 peso-bills, one P50 peso- bill, and three P100 peso-bills in a wallet. If a peso…

A: We want to find probability of drawing a face value greater than 40.

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Q2) Solve the D.E x²dy + (3xy – 1)dx = 0 %3D -

A: Given differential equation is x2dy + (3xy-1)dx = 0

Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: = find area inside r=2cose and outside r 1?

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Q: Show that the equation dy + 2k possesses solutions of the form E c, e cos (a,x+&,) cos (w,t+ 8,)…

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Q: dy given x = sin (x + y). dx Determine

A: Given ,  x=sin(x+y) we have to find differentiation of y with respect to x.

Q: An impossible event

A: This is a probability question. An impossible event means which cannot happen whatever matter it is.…

Q: Q3) Evaluate triple integral f, S, ya(x² – y²)dz dx dy.

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Q: Find plane area inside polar function r 2 and outside polar function r= -2sint in thisd quurter.

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Q: Q4) Find plane area inside the polar function r 2 and outside polar function r=2 sin ( +e) in second…

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Q: 3+ V9 – 4(3 – i) 21 = 3+ V4i – 3 2 How do you solve for the equation above ?

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