1. Solve the system Ax = b for %3D [2 0 1 A = |0 1 0 b = b2 |b3 4. 2 3 using the following steps: (a) (* - * . Compute factorization A = LU. (b) ( it). Solve Ly = b by forward substitution. (c) : is). Solve Ux = y by backward substitution. 1). What is the solution of Ax = b? (d)

Q: 2. Solve the following equation using LU factorization with partial pivoting. + x + 2x, + 2x, = 6 +…

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Q: 5ab(for 3a), 6(for 3a), 7(for 3a), 14(for 3a)

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Q: C. 4. Debbie solved the linear equation 3(x + 4)- 2 16 as follows: %3D (Line 1] S•4)-2.16 (Line 2]…

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Q: . Solve the yn+2+4Yn+1-5Yn coefficients = n2"+2" using method of undetermined

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Q: 2. Find the roots of 3x -9x + 2 = 0. Solution: 3x2- 9x = 3(x2-3x + 19 3(x-, 4. X1 =- and X2 = 2. 3I2

A: To find: the roots of the given equation

Q: i) f(x) = -2x³+ 8x ï) f(x) = x + 2 %3D y 4- 4 3 3 2- 2- 1- 1. 3 1 2 3 4 -4 -1 1 3 5 1- -2 2- 3- 3 -4…

A: The given functions are i) f(x)=-2x3+8xii) f(x)=2x+2iii) The given system is x2+y2=5 and y=2x

Q: w2 – w + 6 dw w3 + 3w 2.

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: у (х + у+ 1)dx +x(х+3у+2) dy %3D0

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Q: 3. Find the general solution of 2ху? + 4 %3D 2(3 — x?у)у'. А. X2у2 + 4х — бу %3D С B. x²y? – 4x – 6y…

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Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: (b) x2n - 2y5n x5n + 4y=n 1/3

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Q: Give the solution of (2x + 3y + z = −1 3x + 3y + z = 1. (2x + 4y + z = -2

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Q: 2. Show that x4 - 3x - 1 has a solution between 1 and 0, and another solution between 1 and 2.

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Q: III. Give the solution of (2x + 3y + z = -1 3x + 3y + z = 1. (2x + 4y + z = -2

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Q: A4: Solve the linear/quadratic system; SE, \E2 x² = 2y – 6 y - x = 2

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: Is  (6, 2)(6, 2) a solution of  x−5y=−3x−5y=−3?

A: Consider the given equation for x and y:

Q: Q. 6. (b) Describe Newton Raphson method for solving the system of non-linear equation. Use NR…

A: We have to describe Newton Raphson's method for solving the system of non-linear equations.

Q: Q1 / From the following table , find f(3) 5 10 15 20 y 1 1.6 3.8 8.2 15.4

A: Use any numerical interpolation technique to obtain the result.   Use Newton's forward difference…

Q: Solve S(y + 1) + S(2y -5) = 3

A: Given equation: y+1+2y-5=3 Concept: Here we shall first remove the root by squaring both sides.…

Q: 4. Is (1,5) a solution of 3x-2y S-4

A: Let's find.

Q: what is the solution of the first order difference equation y(k+1)=y(k)+5

A: Given: yk+1=yk+5

Q: [o1] Write the following system X' = X - 2 3 X (0): %3D as a second order D.E , then solve it .

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Q: Solve for the values of x₁, x₂ and x3using: 0.30x₁ +0.52x₂ +1.50x3 = -0.01 0.50x₁ + 1.25x₂ +0.25x3 =…

A: Gaussian Elimination: The augmented matrix of the given system is changed to reduced echelon form…

Q: Give the general solution of (3D5-13D4 +34D³-46D² +27D-5)y=0

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Q: 1.3.1 Use elementary operations to solve the system of equations 3x +y = 3 x + 2y = 1.

A: 3x+y=3x+2y=1

Q: If E(X) = -2 and V(X) = 6 (i) E (5X – 2) = 5 E(X) – E(2) = (5 x (-2)) – 2 = -12 (ii) V (5X – 2) = 52…

A: As we know that Var(X)= E(X^2)-[E(X)]^2 This implies E(X^2)= Var(X)+[E(X)]^2

Q: 2 2 3 -4 find, Alel. -1 g? A= 3 -2

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

Q: (17) Find the solution of the following second-order difference equation: an+2 – 4an+1+ 8an = 0, ao…

A: Difference equation we can easily solve using auxiliary equation.

Q: 6- Show that y = xsinx is a solution to y +y 2cosx

A: The given differential equation is: y''+y=2 cos x