For the following linear system, use Gaussian Eliminations and the concept of rank to determine the...
Use the Gaussian elimination method to solve each of the following systems of linear equations. In each case, indicate whether the system is consistent or inconsistent. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. 1-5x1 – 2x2 + 2x3 = 14 *(a) 3x1 + x2 – x3 = -8 2x1 + 2x2 – x3 = -3 3x1 – 3x2 – 2x3 = (b) -6x1 + 4x2 + 3x3 = -38 1-2x1 +...
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. x1+ax2−x3 = 2 −x1+4x2−2x3 = −5 −2x1+3x2+x3 = −4 No Solutions: Unique Solution: Infinitely Many Solutions:
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
* Question Completion Status 5. a). Solve homogenous system Ar=0) b). Determine Rank(A), Null(A) and Dim(A) for the coefficient matrix A. c). What is the geometrical interpretation of the solu- tion? 21 – 2x3 + 24 = 0 2x1 + 3x2 + x3 – 2x4 = 0 3.11 + 322 — X3 – 24 0 -21 + 213 – 14 = 0 Yes cono 5. a). Solve homogenous system Ar-0 b). Determine Rank(A), Null(A) and Dim(A) for the coefficient matrix...
Use MATLAB to solve question 7 For the following system of linear equations, use MATLAB of solution or no solution exists. Accordingly, take the appropriate action. Explain your answers 1. to determine whether a unique solution, infinite numbe 3X1 + 4X2 + 2X3-X4 + χ5 + 7x6 + x,-42 2X1-2X2 + 3x3-4X4 + 5X5 + 2x6 + 8x7-32 x1 + 2x2 + 3x3 +x4 + 2x5 + 4x6 + 6x7 = 12 5x1 + 10x2 + 4x3 + 3x4 +9X5-2X5...
Use the Gaussian Elimination Algorithm to solve the following linear systems, possible, and determine whether row interchanges are necessary. 3x – X2 – Xz + 2x4 = = -3.4x; – x2 – 2x3 + 2x4 = 1,x1 + x2 + x4 = 2, 0,2x1 + x2 – X3 + X4
Use Gaussian elimination to solve the equations 4.21 + 4.22 - 2x3 = -1 3x1 + 4x2 – 3x3 = 3 -2x1 - 3x2 + x3 = 1
Use a software program or a graphing utility to solve the system of linear equation solve for X1, X2, X3, and x4 in terms of t.) x1 - x2 + 2x3 + 2x4 + 6x5 = 13 3x1 - 2x2 + 4x3 + 4x4 + 12x5 = 27 X2 - X3 - X4 - 3x5 = -7 2x1 - 2x2 + 4x3 + 5x4 + 15x5 = 28 2x1 - 2x2 + 4x3 + 4x4 + 13x5 = 28 (X1,...
Determine all values of the constant k for which the following system have; a) No solution b) Infinite number of solutions x1 + 2x2 –x3 = 3 2x1 + 5x2 +x3 = 7 x1 + x2 –k2x3 = -k
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. ax1−5x2+5x3 = 10 −3x1+4x2−x3 = −9 x1+2x2+7x3 = −6 when does it have.... No Solutions: Many Solutions: