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FEL 1120 Linear Systems 2016 PART NO. 1. SOLVE THE FOLLOWING PROBLEMS Problem No. Solve the following system of linear equations using elementary row operations (do not use matrices when solving it) Show every step when modifying the system to REF 2. Show REF of your system 3. Show all steps to modify the system to 4. Show RREF of your system 5. Write the solution ( y-2v + x + 3y + 2z = 1 -V + 2x +...
5. (15 pts) For the linear system x + 2y + z = 4 2 + 5y + 2z = 3 4x - y +9z = -1 a) Write the system in matrix-vector form Ax = b. b) Form the augmented matrix [ A6] c) Fill-in the necessary row operations to produce each of the following matrices. 4 1 2 1 0 -3 -1 0 9 -5 17 → O CON 1 00-8 4 -1 20 1 2 1 4...
In exercises 9-18 apply elementary equation operations to the given linear system to find an equivalent linear system in echelon form. If the system is consistent then use back substitution to find the general solution. See Method (1.11) and Method (1.1.2) 4x + 3y + z = 0 3x + 2y + z = -2 10. 3x-5y + 2z =-1
Find the basis and the dimension of the following linear solution system: x + y + z = 0, 3x + 2y – 2z = 0, 4x + 3y – z = 0 and 6x + 5y +z = 0
7. Solve the system of equations below using matrices (row operations). If the system has no solution, say that it is inconsistent. Include your work. 2x + y = -4 -2y + 4z = 0 (3x - 2z = -11
Use Cramer's Rule to solve (if possible) the system of linear equations. (If not possible, enter IMPOSSIBLE.) 4x - 2y + 3z = -11 2x + 2y + 5z = 1 8x - 5y – 2z = 10 (x, y, z) = (I
1. Consider the following system of linear equations: (8 marks) x+y = 3 7 7 2 -x+z=2 y-w=1 W = 4 z + w = 4 1) Use Gauss-Jordan elimination to put the augmented matrix corresponding to this system into reduced row echelon form. Clearly show all the elementary row operations applied. (3 marks) 12 nn
2. Find the augmented matrix of the linear system X – y + z = 7 x + 3y + 3z = 5 X – Y – 2z = 4 Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
For what values of m and n the following system of linear equations has no solution? ( 3x + y + 22 =2 3-2x+2y=3z = 1 (x -y + mzan a) m= &n=- b) m = 2 & n - 1 2 d) m= & ner c) m &nER
A linear system may have a unique solution, no solution, or infinitely many solutions. Indicate the type of the system for th following examples by U , N , or I7x+3y= pi 4x-6y= pi^2 2x+3y= 0 4x+6y= 0 2x+3y=1 4x+ 6y= 1x+y=5 x+2y=102x-3y=5 4x-6y=10