For the linear system
x+ 3y = 4
4x + hy = -2
a) Place the augmented matrix [ A | 6 ] in RREF. (Fill-in the row operation used and the bottom row of the matrix)
b) For what value(s) of h does the system not have a solution?
c) For what value(s) of h does the system have exactly one solution?
Find the augmented matrix of the linear system X +y+z= -8 X – 3y + 3z = -4 X – Y + 2z = -6. 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.
Consider the linear system in three equations and three unknowns: 1) x + 2y + 3z = 6, 2) 2x − 5y − z = 5, 3) −x + 3y + z = −2 . (a) First, identify the matrix A and the vectors x and vector b such that A vector x = vector b. (b) Write this system of equations as an augmented matrix system. (c) Row reduce this augmented matrix system to show that there is exactly...
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.
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
2. Consider the linear system -2.c + 3y + 2 = 5 4.c +9y-322 = 5 -2.c + 18y - 292 = 20 (a) Write down the augmented matrix of the linear system. (b) Find the reduced row-echelon form of your matrix from part (a). (c) Using your answer to part (b), write down the solution to the linear system. Clearly indicate which variable(s) (if any) you are using as a free variable(s).
For the linear system 3x + 2y + 10z = -6 x + 2z = -4 y + 2z = 3x + 4y + 10z = 8 a) Use your calculator to place the augmented matrix in RREF and write it here. b) Find the general solution to the linear system, written as either the vector equation of a line or the vector equation of a plane.
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...
Solve these two systems of linear equations questions
A
B
x + 3y + 4z = 3 2.c + 7 + 72 = 4 3x + 13y + 8z = 1 3 Let the reduced row-echelon form of the augmented matrix, representing a system of four linear equations in the five unknowns r, s, t, u, and V, be as shown. Write out the general solution of the system of equations. 1 0 9 0 7 0 1 8 0...
1. Graph the system of linear equations. Solve the system and interpret your answer 3y 2 -+2y 3 2. Solve the system of linear equations for and y (Cos ) x(sin 0) y = 1 (sin 0) x (cos 0) y = 1 3. Use back substitution to solve the system. 6r23r =-3 r22r3 1 3-2 4. Slove the given system by Gaussian elimination.. 4x1-2+x3-1 +2x2-3r3 = 2 2x 3= 1 5. Identify the element ary row operation (s) being...
Consider the following system of linear equations. x1 + 2x2 = 2 x1 – x2 = 2 x2 = 1 (a) Give a brief geometric interpretation of the solution set of the system. (b) By hand, find the RREF of the augmented matrix of the system, indicating the row operations you are using at each step. (c) Is the system consistent? (d) Find the solution set of the system.