Given a system of linear equations: w + 2x - 3y + 4z = 1

Question

Question

Given a system of linear equations:

w + 2x - 3y + 4z = 1

3w + 6x - 9y + tz = 2

(i) Express the system in [A][b] form.

(ii) Determine the value of t such that:

- the system is consistent; and

- the system is inconsistent.

(iii) Determine the rank of A, and by using the Rank Theorem, determine the number of free variables.

math algebra

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Consider the system of equations shown below. 3w - 2x + 16y - 27 = -9...

Consider the system of equations shown below. 3w - 2x + 16y - 27 = -9 -W + 5x - 14y + 18z = 93 3w - x + 14y + 2z = 1 (a) Determine whether the nonhomogeneous system Ax=b is consistent. O consistent Inconsistent (b) If the system is consistent, then write the solution in the form X Xp + Xn, where X, is a particular solution of Ax = b and X, is a solution of AX...
Consider the system of equations shown below. 3w - 2x + 16y - 22 = -8...

Consider the system of equations shown below. 3w - 2x + 16y - 22 = -8 -w + 5x - 14y + 18251 3w - x + 14y + 22 = 1 (a) Determine whether the nonhomogeneous system Axb is consistent O consistent Inconsistent (b) If the system is consistent, then write the solution in the form x = x + xh where x is a particular solution of Ax=b and is a solution of AX -0. (Ift x =...
Consider the system of equations shown below. 2x - 4y + 5z = 10 -7x +...

Consider the system of equations shown below. 2x - 4y + 5z = 10 -7x + 14y + 4z = -35 3x - 6y + z = 15 (a) Determine whether the nonhomogeneous system Ax = b is consistent. O consistent O inconsistent (b) If the system is consistent, then write the solution in the form x = Xp + xn, where xp is a particular solution of Ax = b and xn is a solution of Ax = 0....

3. Consider the following system of linear equations: 2x + 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....
20. [-13.22 Points] DETAILS LARLINALG8 4.6.054. ASK YOUR TEACHE Consider the system of equations shown below....

20. [-13.22 Points] DETAILS LARLINALG8 4.6.054. ASK YOUR TEACHE Consider the system of equations shown below. 3w - 2x + 16) - 2z = -9 -W + 5x - 14y + 18z = 37 3w - X + 14y + 2z = 1 (a) Determine whether the nonhomogeneous system Ax = b is consistent. O consistent O inconsistent (b) If the system is consistent, then write the solution in the form x = Xp + Xh, where xp is a...
5. For the system, 4x + y + 2z = 1 2x + 3y + 4z...

5. For the system, 4x + y + 2z = 1 2x + 3y + 4z = -5 x – y +3z = 3 Find the rank of the coefficient matrix by calculating the determinant. Use Cramer's theorem to find the solution of this system. (10 points) 6. Find the inverse of the following matrix using Gauss-Jordan method. Verify your result by computing the inverse using the method of determinants. (10 points) 1 2 4 2 4 2 1] 1...

2) The row echelon form of a system of linear equations is given. a) Write the...

2) The row echelon form of a system of linear equations is given. a) Write the system of equations corresponding to the given matrix. Use x, y, z; or X1, X2, X3, X4 as variables. b) Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. 1 0 2 4 0 1 -1 2 1] 2 [1 2 317 i) 0 14 21 Lo o 03] il) 0 0 i 2 0 42] 10 1...
Solve these two systems of linear equations questions A B x + 3y + 4z =...

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...
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of...

Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...

Solve the system. If a system has ope unique solution, write the solution set. Otherwise, determine...

Solve the system. If a system has ope unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. 2x+3y+5z=-23 -4x+2y+4z=9 -6x=y+13z=-5 Select one: a{(-1, -2, -3) b. Infinitely many solutions, dependent a. No solution, inconsistent