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

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

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations $\{\begin{array}{l}9x-3y+z=13\\ 12x-8z=5\\ 3x+4y-z=6\end{array}$

Write the vector form of the general solution of the given system of linear equations. ${\displaystyle x_1-x_2-2x_4-x_5+4x_6=0}$

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 $x_1,x_2,x_3,x_4$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. ⎡⎣⎢100010430420⎤⎦⎥

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. 7 x-5 y=11 x-y=-5

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 $x_1,x_2,x_3,x_4$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
$\left[\begin{array}{ccccc}1& 0& 0& 0& 1\\ 0& 1& 0& 0& 2\\ 0& 0& 1& 2& 3\end{array}\right]$

Determine whether the statement is true or false. Justify your answer. You cannot write an augmented matrix for a dependent system of linear equations in reduced row-echelon form.