3. Solve the linear system belowa + 2b – c + 4d—а — 3b + 2с + 2d — 42а + 2b — с + 2d 3D 21%3D-a%3Da + 2b + c = 1using,a. Cramer's Ruleb. Gaussian Eliminationc. Gauss-Jordan method

Answered: Image /qna-images/answer/f8a44e41-ef2f-47fb-b589-a5472a8a2717.jpg

Answered: 3. Solve the linear system below a + 2b…

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

4. Solve by Matrix Inversion. * For this number, solve using X = (A-1)B 2w – 2x + 3y + 4z = 33 3w – 5x – 7y + 3z = 11 4w + 3x – 4y – 5z = 3 5w + 4x + 6y – 2z = 45 1 Add file
1. (a) Use definition of linear transformation to determine whether the transformation T:R? → R³ defined as follows is linear. -y T r+ 2y 2.r – 4y (b) Let T : R" → R" be a linear transformation. i. Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify. ii. Does S(0) = 0 mean that S is linear? If not, can you give a counter-example? (c) Consider the following matrix transformation T : R² → R² defined as a b T d i. If T rotates the 2D space 150° counter-clockwise, and then reflects the result across the new r-axis, find a, b, c, d. ii. What if T reflects the 2D space across the r-axis first and then rotates 150° counter-clockwise? Do you expect to get the same a, b, c, d? Why or why not?
2x + y + z = 10 Зх + 2у + 3z %3D 18 X + 4y + 9z = 16 [CLO1] The first step to solve the above linear system using Gaussian Elimination is to apply the following: row2 = row2 - m21 * row, Then, to apply the following: row3 = row2 – m31 * row, What are the values of m21 and m31? m21 = m31 =
2) Solve the following system of linear equations by using Cramer's Rule. 2x+0y+12 z= 5 0x-5y+9z=20 15 x+ 10 y+2 z = 2
Q1// Solve the following simultaneous equations using: 1. Method of Addition/subtraction 2. Method of substitution 3. Graphing 4. Matrix method. 2x – 21 = 0, 2y – 31 = 0 and 2x – 3y – 5=0
I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3
4. Use Gaussian elimination with backward substitution to solve the following linear system: 2x1 + x2 – x3 = 5, x1 + x2 – 3x3 = -9, -x1 + x2 + 2x3 = 9;
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. a) Given the following system of linear equations: -6+ 10 *+y+=5 2x-y+=9 x-2y+3z =16 Detemine the values of x, y and z using the Cramer's rule.
1. Is the following system consistent ? Provide a justification for your decision.Ensure that you explain each step in the computation.2. Can Cramer's rule and the matrix inversion method be used to solve the system? Justify your response.
(c) Consider the system 2х1 — бх, — Хз — 38 — Зх1 — х2 + 7Хз :-34 -8x1 + x2 – 2x3 = -20 (i) Write the system in AX = B. 1 0 | and 23/10 1. (ii) Given the decomposition of matrix A is L= -3/2 -4 -6 -1 -43 b -11 -5 a 1 U = (0 -10 and the Al: 11/2 -373/20, -62 373 -11 C -20/ Find a, b and c.

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

3. Solve the linear system below a + 2b – c + 4d = 1 —а — 3b + 2с + 2d — 4 2а + 2b - с + 2d — 2 - %3D | a+ 2b + с %3 1 using, a. Cramer's Rule b. Gaussian Elimination c. Gauss-Jordan method