Question

Write the vector form of the general solution of the given system of linear equations. 3x_1+x_2-x_3+x_4=0 2x_1+2x_2+4x_3-6x_4=0 2x_1+x_2+3x_3-x_4=0

Forms of linear equations
ANSWERED
asked 2020-12-17
Write the vector form of the general solution of the given system of linear equations.
\(3x_1+x_2-x_3+x_4=0\)
\(2x_1+2x_2+4x_3-6x_4=0\)
\(2x_1+x_2+3x_3-x_4=0\)

Answers (1)

2020-12-18
\(\begin{bmatrix}3&1&-1&1&0\\2&2&4&-6&0\\2&1&3&-1&0\end{bmatrix}\)
Write the augmented matrix of the coefficients and constants
\(\begin{bmatrix}1&0&0&2&0\\0&1&0&-5&0\\0&0&1&0&0\end{bmatrix}\)
Transform the matrix in its reduced row echelon form.
\(x_1=-2x_4\)
\(x_2=5x_4\)
\(x_3=0\)
\(x_4=x_4 \text{ free}\)
Determine the general solution
\(\begin{bmatrix}x_1\\x_2\\x_3\\x_4\end{bmatrix}=x_4 \begin{bmatrix}-2\\ 5 \\ 0 \\ 1 \end{bmatrix}\)
Rewrite the solution in vector form
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-06-25
The row echelon form of a system of linear equations is given.
(a)Writethesystemofequationscorrespondingtothegivenmatrix.Usex,y;orx,y,z;or x_1,x_2,x_3,x_4 asvariables.
(b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution. \left[ 10215−1 \right]
asked 2021-06-24
Write the vector form of the general solution of the given system of linear equations.
x1+4x4=0
x2−2x4 ​
asked 2021-06-10
Determine whether the given set S is a subspace of the vector space V.
A. V=\(P_5\), and S is the subset of \(P_5\) consisting of those polynomials satisfying p(1)>p(0).
B. \(V=R_3\), and S is the set of vectors \((x_1,x_2,x_3)\) in V satisfying \(x_1-6x_2+x_3=5\).
C. \(V=R^n\), and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
D. V=\(C^2(I)\), and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.
E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.
F. V=\(P_n\), and S is the subset of \(P_n\) consisting of those polynomials satisfying p(0)=0.
G. \(V=M_n(R)\), and S is the subset of all symmetric matrices
asked 2020-12-28
Write the vector form of the general solution of the given system of linear equations.
\(x_1+2x_2-x_3=0\)
\(x_1+x_2+x_3=0\)
\(x_1+3x_2-3x_3=0\)
asked 2021-05-18

Write the vector form of the general solution of the given system of linear equations.
\(x_1+3x_2+2x_4=0\)
\(x_3−6x_4=0\)

asked 2021-06-24

Write the vector form of the general solution of the given system of linear equations.
\(x_1+2x_2−x_3+x_4=0\)

asked 2021-05-03
The reduced row echelon form of the augmented matrix of a system of linear equations is given. Tell whether the system has one solution, no solution, or infinitely many solutions. Write the solutions or, if there is no solution, say the system is inconsistent. [1200−4 0010−3 00012 00000]
asked 2021-05-23
The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
asked 2021-06-29
The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. ⎡⎣⎢100010010430230⎤⎦⎥ ​
asked 2021-05-05
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y;x,y; or x,y,z;x,y,z; or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [1001−40][
...