1. The system of equations given by211 + 2r2 + I3 = 5,2i + 3r2 +a3 = 2,3z + 472 + 523 =1,is written in matrix form as1 32.5.42112 2 13 13 4 512312 11123 4 51232 2 11= (5 2 1)3 4

We are given the system of linear equation which we need to convert into matrix form 2x1+2x2+x3=5…

Answered: 1. The system of equations given by 2z,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

6). Determine the solution for the following augmented matrix for a 3x3 linear system of equations. y r3 6. (x, y, z) = ( ) -9 18 Lo 7 | 14. O ON
Find the LU factorization of A = and then use it to solve the system -4 -3 3 16 15 -11 A = x1 = x₂ = x3 = 8 -6 -8 || x1 x2 x3 = -4 -3 3 16 15 -11 8 -6 -8 -31 127 44 " such that the matrix L has ones along the diagonal,
6. Suppose the augmented matrices below correspond to either a system of linear equa- tions in 2 variables (x, y) or system of linear equations in 3 variables (x, y,z). These matrices may or may not be in RREF. You you need to in order to determine the solutions. NOT need to put them into RREF unless What are the solutions to the system? If there are solutions, please write your answer as (x, y) or (x, y,z). If there are infinitely many solutions, please write your point in terms of one variable (you may choose the variable). 1 0 0 1 -7 0 0 2 (a) 1 -6 1 0 0 0 1 0-4 0 0 1 9 (b) 9 1 0 (c) 0 1 -4 0 0 1 0 -4 (d) 0 1 -3 1 5 7 0 0 0 0 0 0 (e)
1. In each part of this question, you have been given a system of equations and the corresponding matrix taken to RREF. Write the general solution as a vector equation. • List the basic solutions. a. b. (x₁ - x₂ + 2x4 = 0 [1 -X₁ + x₂ + 3x3 - 11x4 0 2x₁ - 2x₂ + 4x4 0 0 -4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo - = 0 " -1 0 2 01 0 1 -3 0 0 0 0 0 0 00 (3w+9y15z = 0 1 0 -14w + 33x - 75y - 62z = 0 0 1 -5w+ 14x - 29y - 31z = 0 0 0 (52w 164x + 320y + 396z = 0 Lo 0 3 -1 -4 0 0
3. Consider the system of linear equations 2x₁ + 3x₂ + x3 = −1 3x₁ + 3x₂ + x3 = 1 3x₁ + 4x₂ + x3 = -2 a. Find the inverse of the coefficient matrix A. b. Using the inverse matrix of A, find the solution of the system. 4. Suppose the following matrix A is the augmented matrix for a system of linear equations A = 1 2 3 4 2 -1 -2 a² -1 -7 -11 a where a is a real number. Determine all the values of a so that the corresponding system is consistent.
Consider the following linear equations: -5x + 5y +7z : 3 = 5 -5x+(21-k)y + 6z -5x + 5y + (11- k)z =k+11 a) X1 Suppose the above equation is expressed as Ax = b with x = X2 X3 equations in one matrix form as (A[b)= -5 5 7 124 -5 -5 Express the coefficients of the 3
5. Solve the system of equations 3z-2z + 2z = 10 a + 2 - 3z, = -1 4 + za+2, = 3 %3D (a) by Cramer's rule and (b) by using inverse matrices.
In the given matrix equation, x + y = -1 -21 -2 0 1 2 3 GRA 13 - [ ] = y 20 X 7 1 5
2. Solve the following system of linear equations by first finding the LU factorization of the coefficient matrix: x₁ + 2x₂ + 3x3 = 2 2x₁x₂ + x3 = 4 -x₁ + 4x₂ 3x3 = 1
Q1.Express the following system of equations in matrix forms and solves them by the elimination method (Gauss Jordan Method). i. x, + 2x, + x; = 2 3x, + x, – 2x3 = 1 4x, - 3х, — х, — 3 | 2x, + 4x, + 2xz = 4
2. The augmented matrix for the system of equations 211 + 2r2 + I3 = 5, 2i + 3r2 + a3 = 2, 3r1 + 4r2 + 5z3 = 1, is given by O (2 2 1 1 4 5 2x 2x2 3r2 3z, 4r2 5z3 1 2 2 1 3. 1 2 4 5 1 '5 2 2 1 2. 3 4 5 1 1 1 213 213

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

1. The system of equations given by 2z, + 273 + z3 = 5, 2 +3z3 +z3 = 2, 3r + 4z, + 5z3 = 1, is written in matrix form as O (2 1 3 2 3 4 5 %3D (1 1 O (2 2 1 1 3 1 3 4 5 (2 2 1 5) |1 3 1 2 (3 4 5 1 2 2 1 (11 I2 I3) |1 3 1 = (5 2 1) 34 %3D