3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx...
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w....
4. Solve the following system of linear equations using Gauss-Jordan elimination: X1 + 32 - 2x3 + 24 + 3x5 = 1 2x 1 - X2 + 2x3 + 2x4 + 6x5 = 2 3x1 + 2x2 - 4x3 - 3.24 - 9.25 = 3
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...
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Consider the linear system x1 + x2 – 2x3 + 3x4 = 0 2x1 + x2 - 6x3 + 4x4 -1 3x1 + 2x2 + px3 + 7x4 -1 X1 – X2 – 6x3 24 = t. Find the conditions (on t and p) that the system is consistent, and inconsistent. If the system is consistent, find all the possible solutions (including stating the dimension of the solution space(s) and describe the solution space(s) in parametric form).
Help with system of linear equations. Question 11 [10 points] Solve the following system of linear equations 2x1-4x2 2x3+4x46 2x1+5x2+x3-5x4 12 x1+3x2+x3-6x 11 -2x1+6x2-x3-2x4 -14 if the system has You can The system has no solution no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. appropriate) by clicking and dragging the bottom-right corner of the matrix. Row-echelon form of augmented matrix: 0 0 0 Official Time: 16:52:07 SUBMIT AND MARK
Solve the system of linear equations using the Gauss-Jordan elimination method. 3x1 2x2X316 x1 + 2x2 + 2x3 = 12 (X1, X2, X3) =
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 +...
Consider the following. (x1 - x2 + 4x3 = 20 3x + 332 = -4 -6x2 + 5x3 = 32 (a) Write the system of linear equations as a matrix equation, AX = B. 14 X1 I X2 = IL X3] (b) Use Gauss-Jordan elimination on [ A B] to solve for the matrix X. X2
Problem #4 Given the following system of linear equations: 2 x1 6x2 X3 = -38 -3 xI - X27 x3 = -34 -8 xix2 2x3 = -20 Use Gauss-Jordan method to solve for the x's