Q.2 Solve the following set of equations x + 4 y + 3z = 2, 2x - 6 y + 6z = -3, 5x - 2 y + 3z = -5 %3D (a) By using Cramer's rule (b) Verify your answer by using ordinary algebra method

Q: 2. 21 Зу 6 Solve : =+ x 3y 3 2 -+==0 х у and hence find 'a' for which y = ax - 4

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Q: Question 1. Find the roots of the linear equations using Cramer's Method 5X1 + 4X2 + X3 = 3.4 10X1 +…

A: To find the root of the linear equation using cramer's rule .

Q: solve the following simultaneous equation using cramer's rule": 2x-y = 3 3x+2y = 8

A: To solve the simultaneous equation by Cramer's rule we first find co-efficient matrix , X-matrix,…

Q: Question 12 Use the Method of Undetermined Coefficients to determine the form of the particular…

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Q: S xdx can be solved by either algebraic subsitution or integrataion by parts. Vx- 1 A True B False

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Q: Theorem 5 Every solution of Eq. (1) is unbounded if a > 1. Proof: Let {rn}-4 be a solution of…

A: The determined green part has been explained in detailed in step 2 and step 3.

Q: Question 8 If E = 2ax + ay - 3az, F = ay - az, and G = 3ax + 5ay + 7az, determine, E - 2F + G. А)…

A: Given that E=2ax+ay-3az,  F= ay-az    and  G=3ax+5ay+7az. We have to determine E-2F+G

Q: Find the pasticulao Solution of the ng Anitial Value Problem bting 8- 1) =2 %3D

A: We have to find the particular solution of the initial value problem dydx+12xy=xy-8 with the initial…

Q: Solve the given Bernoulli DE: 3y' + 3y/x = 2x4y4

A: A detailed solution is given below

Q: Q1\calculate x1, x2, xn from the following equations: -3x1 + 9x2 + Xn = 2 5x1 - 2x2 + 3x,n = -1 2x1…

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Q: Solve the following problem ди = 0 ; x € (0,1) ,t > 0, u(0, t) — и(1,t) — 0, u(x,0) = x

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Q: (1) Compute A-1. (2) Use A-1 to solve the s x1 + 3x2 = 4 (a) 2x1 + 5x2 = 3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: b. Solve the following equations using Cramer's Rule 4x + 2y = 10 Зх— 5у %3D 1

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Q: 2. Find the inverse of A = 1 1 1 1 2 -1 3 1 -1 2 3 H2H2 1 using Gauss-Jordan method.

A: The solution is given as

Q: 4. Give the general solution of the equation Ax = b in standard form. 1 3 *a. A = 2 1 b 1 2 2 -1 b.…

A: (b) We have to find the general solution of the equation Ax=b, where A and b are as follows - A =…

Q: Q4 -A// Solve the following system by using Cramer's rule: 4 y+ 2tan(x) = 6 5 tan(x) - 2 y = 3 B//…

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Q: 2. Find the inverse of A = == CN 2 1 -1 3 - -1 2 2 22 12 3 2 using Gauss-Jordan method.

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Q: Solve the equations Ax = b using Jacobi Method

A: To find- Solve the equations Ax = b using Jacobi Method A =…

Q: Find the general solution of the following:

A: Given equation  (y+1)dx+(4x-y)dy=0write the equation in the form of dx/dy(y+1)dx=-(4x-y)dydivide…

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A: Given the three systems s1,s2 ,s3 as a response to a complex exponential input ej5t. Such a that…

Q: (2) Solve the following PDE for u(x, y): a'u 1- +30u 18x-3x +2

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Q: The particular solution of the following equation by using the D Operator y" +2y' + 3y -2x +3 2 13 2…

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Q: у" + 2y' + 3у 3D 0

A: We need to find the general solution of the differential equation y''+2y'+3y=0

Q: 1. Find the general solution to the following equations fip° (a) x + 2y = x-3.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Solve the equation Ax = b by using the LU factorization given for A. 1 2 3 1 0 0|| 1 2 3 0 11 0 2 0…

A: The given matrix equation can be written as:  LUx=B OR…

Q: 2/ The following system of equations is designed to determine voltages in a circuit, solve this…

A: As instructed, we shall use the Gauss-Jacobi method to perform iterations over this system of linear…

Q: Solve the following ODF y +y -2y = 2 e2x a. C1 e* + C2 e2x - e 2x / 3 b. C1 e* + C2 e2x - 2 e2x / 3…

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Q: 1. Using Gauss-Jacobi, compute a solution to the problem Ax=b where 2-4 7 3 2 49 -2 A = 8 7 b= 16 23

A: Given : A =2-4783249-2      b=71623                  AX= b To find : The solution of problem by…

Q: Find the general solution of the following DE in explicit form. y' =3+2/y-3x +12.

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Q: Solve the following system of three equations using Jacobi Method. Assume initial value of unknowns…

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Q: -) Solve the following Cauchy problem: -00 0, u(x, 0) = 1, u4(x,0) = 2 – e¯*, -0 <x< oo. 4 uzz;

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Q: Solve the given set of equations by applying SOR methods with w=1.2 (assume „(0) (0) X3 (0) = 0.0…

A: We know that for symmetric positive definite matrix the SOR method converges for values of the…

Q: 2 In x 1 e* 2 1 In 2x -1

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Q: Solve the following equations by Jacobi Iteration Method. 8 X₁ + X₂ X3 = 8 X₁ 7 X₂ + 2 X3 = -4 2X₁ +…

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Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: (b): Solve the following initial value problem by the undetermined coefficients (Superposition…

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Q: Example 2-13; solve the following DE j+ 3ỹ + 2y = 10e3x + 4x²,

A: To find a General solution of the given differential equation we have to find a complementary and…

Q: Solve the following equations by using Cramer's Rule 2x + 2y + z = 1 x-y + 6z = 21 3x - 2y-z = 4

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Q: 17. Solve the system of equations using Cramer's Rule. 2x + y = 1 5x + 2y = 5 |Dxl X = IDI IDyl…

A: The given system is: 2x+y=15x+2y=5

Q: 1. Solve the following systems of equations using the a. Inverse Method b. Cramer's Rule c.…

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Q: (D² + 16)y = 4sin3xcosx

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Q: 2.40 Solve the following problem for x (t) and y(t): x = -2x + 5y y = -6y - 4x + 10us (1) x(0)=5…

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Q: 1. (a) Use Cramer's rule to solve for y in the SLE: 4х + y + 6 Зх + 7y 3 - + 2w 7x + 3y + 5z + 8w +…

A: 1.a Given system of equation is 4x+y+z+w=63x+7y-z+w=3x+y+z+2w=47x+3y+5z+8w=20now, we write the…

Q: Solve the following ODF y' +y -2y = 2 e 2x O a. C1 e* + C2 x e²2x - 2 e2x b. C1 e* + C2 e²x - 2 e2x…

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Q: Solve the following ODF y +y -2y = 2 e2x C1 e* + C2 x e2x - 2 e 2x а. b. C1 e* + C2 e2x - 2 e2x / 3…

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Q: Solve the following equations by Gauss-seidel Method. Start at all value x1=x2=x3=x4=1 9X1— 3X2 + Хз…

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Q: 1 1 3 12. Find cofactor C22 of | -2 2 1 0 1 1

A: Minor of an element in a matrix is defined as the determinant obtained by deleting the row and…

Q: Consider the ODE: y" -5y = 2x3 2.x3 4x2 – x +6 While solving this ODE using the method of…

A: We have to consider the ODE: y" - 5y' = 2x3 - 4x2-x+6

Q: 2.10. Solve the following equations: (a) Yk+1 = (k² + 1)yk, (b) Yk+1 = (k – k² – k³)yk, (c) = . - -…

A: One of the properties of the gamma function is given by: Γ(m)=(m-1)Γ(m-1) where, m is any real…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.