For the linear system
3x + 2y + 10z = -6
x + 2z = -4
y + 2z = 3
x + 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.
6. (15 pts) For the linear system 3x + 2y + 10x = -6 3 + 2z = y+2z = 3 3+ 4y + 10% = 8 a) Use your calculator to place the augmented matrix in RREF and write it here. 3 2 10 -6 i 470 - 4 3 8 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...
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...
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...
Write the matrix corresponding to the following system of linear equations. - 8x + 4y = 2 4x - 3y = 6 What is the corresponding matrix? (Do not simplify.) Tes Change the third equation by adding to it (-3) times the first equation. Give the abbreviation of the indicated operation. (x + 4y + 5z = 4 5x - 3y - 2z = 1 3x + 3y + 2z = 1 The transformed system is x + 5x -...
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x – 2y) Submit Answer [-70.71 Points] DETAILS LARLINALG8 6.3.007. Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y, z) = (8x + y,7y - z), v = (0, 1, -1) T(v)
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.
2,3, 6, 7 1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
2 +2y - 2=3, I-y=2, 2.0 + y - 2= 5. 1. Write the system as an augmented matrix and perform some elementary row operations to make it in row reduced row echelon form. 2. What is the rank of the augmented matrix? How many free variables does this system have. 3. Write the solutions of the system in parametric form. 4. Consider the following system 2 + 2y - 2=3, r-y=2, 2.x + y -2=1. (The only difference is...
5. Consider the system of equations: 2 - Y + 2z = 4 3x - 2y + 92 = 14 2. - 4y + az = b. Find all the values of a and b so that the system has a) no solution b) 1 solution e) exactly 3 solutions and 4) infinitely many solutions.